{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<h1 align=\"center\"> Explaining Box Plots </h1>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I was always curious about where the -2.698σ,  -.6745σ, 6745σ, and 2.698σ numbers came from. Consequently I would look it up and find they are from Z Score Tables which are basically tables showing the percentages of numbers coming up in a normal. This post will derive a Z Score table and explain the different parts of a box plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook explains how those numbers were derived in the hope that they can be more interpretable for your future endeavors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import all libraries for the rest of the blog post\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "from matplotlib.patches import ConnectionPatch\n",
    "from scipy.integrate import quad\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAFgCAYAAACmDI9oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4/8AkWVFbtnnmZUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150a4c3bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 3000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize=(10, 5))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes.boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes.set_xlim(-4, 4)\n",
    "axes.set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes.annotate(r'',\n",
    "            xy=(-.73, .205), xycoords='data',\n",
    "            xytext=(.66, .205), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes.text(0, .25, \"Interquartile Range \\n(IQR)\",  horizontalalignment='center', fontsize=18)\n",
    "axes.text(0, -.21, r\"Median\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(2.65, -.15, \"\\\"Maximum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.15, \"\\\"Minimum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-.68, -.24, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.21, r\"(Q1 - 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(.6745, -.24, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(.6745, -.30, r\"(75th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(-.68, -.30, r\"(25th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(2.65, -.21, r\"(Q3 + 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes.annotate('Outliers', xy=(2.93,0.015), xytext=(2.52,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "axes.annotate('Outliers', xy=(-3.01,0.015), xytext=(-3.41,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/simple_boxplot.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6622499999999998"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stuff = (2.65 - .6745) / 2\n",
    ".6745 + stuff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Whiskers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsgAAAFgCAYAAACmDI9oAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIiEiDAZmIiIiISOP/AU8snyqaCpq6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150a4dfc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 3000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 1, ncols = 1, figsize=(10, 5))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes.boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes.set_xlim(-4, 4)\n",
    "axes.set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes.annotate(r'',\n",
    "            xy=(-.73, .205), xycoords='data',\n",
    "            xytext=(.66, .205), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes.text(0, .25, \"Interquartile Range \\n(IQR)\",  horizontalalignment='center', fontsize=18)\n",
    "axes.text(0, -.21, r\"Median\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(2.65, -.15, \"\\\"Maximum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "#axes.text(-1.66, .03, \"Whisker\", horizontalalignment='center', fontsize=18);\n",
    "\n",
    "axes.text(1.66, .06, r'Whisker', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white',\n",
    "                  'edgecolor':'blue',\n",
    "                  'linewidth': 4,\n",
    "                  'alpha': .4,\n",
    "                  'pad':10.0});\n",
    "\n",
    "axes.text(-1.66, .06, r'Whisker', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white',\n",
    "                  'edgecolor':'blue',\n",
    "                  'linewidth': 4,\n",
    "                  'alpha': .4,\n",
    "                  'pad':10.0});\n",
    "\n",
    "axes.text(-2.65, -.15, \"\\\"Minimum\\\"\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-.68, -.24, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(-2.65, -.21, r\"(Q1 - 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "axes.text(.6745, -.24, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes.text(.6745, -.30, r\"(75th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(-.68, -.30, r\"(25th Percentile)\", horizontalalignment='center', fontsize=12);\n",
    "axes.text(2.65, -.21, r\"(Q3 + 1.5*IQR)\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes.annotate('Outliers', xy=(2.93,0.015), xytext=(2.52,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "axes.annotate('Outliers', xy=(-3.01,0.015), xytext=(-3.41,0.20), fontsize = 18,\n",
    "            arrowprops={'arrowstyle': '->', 'color': 'black', 'lw': 2},\n",
    "            va='center');\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/simple_whisker.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it All Together"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "#Integrate PDF from -.6745 to .6745\n",
    "result_n67_67, _ = quad(normalProbabilityDensity, -.6745, .6745, limit = 1000)\n",
    "\n",
    "# Integrate PDF from -2.698 to -.6745\n",
    "result_n2698_67, _ = quad(normalProbabilityDensity, -2.698, -.6745, limit = 1000)\n",
    "\n",
    "# Integrate PDF from .6745 to 2.698\n",
    "result_67_2698, _ = quad(normalProbabilityDensity, .6745, 2.698, limit = 1000)\n",
    "\n",
    "# Integrate PDF from 2.698 to positive infinity\n",
    "result_2698_inf, _ = quad(normalProbabilityDensity, 2.698, np.inf, limit = 1000)\n",
    "\n",
    "# Integrate PDF from negative infinity to -2.698\n",
    "result_ninf_n2698, _ = quad(normalProbabilityDensity, np.NINF, -2.698, limit = 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAKACAYAAAAMzckjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCGEECFGEkAhhBBCiBDz/wHG4eFa6uMO8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150a51c910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(39)\n",
    "\n",
    "# 8, 11, 20\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=True, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='Blue', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='Black'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower box\n",
    "con = ConnectionPatch(xyA=(-.6745, 0), xyB=(-.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper box\n",
    "con = ConnectionPatch(xyA=(.6745, 0), xyB=(.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# lower whisker\n",
    "con = ConnectionPatch(xyA=(-2.698, 0), xyB=(-2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper whisker\n",
    "con = ConnectionPatch(xyA=(2.698, 0), xyB=(2.698, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -.6745, .6745\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result_n67_67*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "##############################\n",
    "a, b = -2.698, -.6745# integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-1.40, .04, r'{0:.2f}%'.format(result_n2698_67*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = .6745, 2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='blue', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(1.40, .04, r'{0:.2f}%'.format(result_67_2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = 2.698, 4 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(3.3, .04, r'{0:.2f}%'.format(result_2698_inf*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "a, b = -4, -2.698 # integral limits\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='green', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly);\n",
    "axes[1].text(-3.3, .04, r'{0:.2f}%'.format(result_ninf_n2698*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/boxplotNormalDistribution.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/68_95_99_rule.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The normal distribution is commonly associated with the normal distribution with the 68-95-99.7 rule which you can see in the image above. 68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook explains how those numbers were derived in the hope that they can be more interpretable for your future endeavors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Density Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able to understand where the percentages come from in the 68-95-99.7 rule, it is important to know about the probability density function (PDF). A PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable’s PDF over that range — that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. This definition might not make much sense so let’s clear it up by graphing the probability density function for a normal distribution. The equation below is the probability density function for a normal distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/probabilityDensityFunctionNormalDistribution.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s simplify it by assuming we have a mean (μ) of 0 and a standard deviation (σ) of 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/pdfNormal_mean0_std_1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the function is simpler, let’s graph this function with a range from -3 to 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Import all libraries for the rest of the blog post\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x = np.linspace(-3, 3, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "fig, ax = plt.subplots(figsize=(10, 5));\n",
    "ax.plot(x, pdf_normal_distribution);\n",
    "ax.set_ylim(0);\n",
    "ax.set_title('Normal Distribution', size = 20);\n",
    "ax.set_ylabel('Probability Density', size = 20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The graph above does not show you the probability of events but their probability density. To get the probability of an event within a given range we will need to integrate. Suppose we are interested in finding the probability of a random data point landing within 1 standard deviation of the mean, we need to integrate from -1 to 1. This can be done with SciPy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math Expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\Huge \\int_{-.6745}^{.6745}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.500006514273\n"
     ]
    }
   ],
   "source": [
    "# Make a PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -.6745 to .6745\n",
    "result_50p, _ = quad(normalProbabilityDensity,\n",
    "                     -.6745,\n",
    "                     .6745,\n",
    "                     limit = 1000)\n",
    "print(result_50p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAAFICAYAAAA75Xj9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4xLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvAOZPmwAAIABJREFUeJzs3XeYVOXZx/HvzdI7CIiAICpqQFQM\nig0VNVhQsCJSLLHGrsmbokYTjdFoYuyKXSmCWKJRVFRssYMgiBUQERAFQbrAsvf7x3PGHZbZ2Zll\nds/uzu9zXXPNnn7P7MyZ+zznKebuiIiIiEj1VCvuAERERESk/JTMiYiIiFRjSuZEREREqjElcyIi\nIiLVmJI5ERERkWpMyZyIiIhINaZkTiQNM2tiZjeZ2SwzW2dmbmZz4o6rLGY2Mor1irhjkYplZmdE\n/+uXK3t7M9s+2rawPMcWkdxQMpdHzOzU6MSb7rGyjH2YmZ1lZu+Y2Y9mtsLMppjZ/5lZ3TTbdTKz\nMWa2xMzWmNn7ZnZUGce6LorpmPK+5hx4ErgE2BZYA3wHLEq3gZk9HMX9SaYHMbPzom1+MrPmmxWx\nSMTMfm1mfzGzXeKOJS5mdqCZjTKzr6Pv1yIzm2Rm/zSzbUqsWzuDc2TyY98MY3g2aZv70qw3L4Nj\nXrwZ78UvzOw2M/s4Onf/ZGZzo/PxnWY20MxaROtun0EspT3uK+P9XG1m35rZh2Z2n5kNNbMG5X1d\nArXjDkBisR5YUsqyVaVtZGZ1gP8AR0Sz1gEbgN2ixwlmdpC7ryyxXSvgLaA9UASsBfYAnjazk9x9\nbIpj7QRcCjzv7k9l8dpyxsy6AYcQ3q/93f3dDDd9CDgZ+IWZ9XT3SRlsc3L0/LS7/5h1sJLPfgQ+\nB+amWPZrYF9gJjCtAo69Ljp2lSuZM7MC4C7gzKTZPwLNgVbAL4FJwJyk5U64YEunGVCfcB4r84LN\nzI4H+mUad2QJ4byTSqnn6DLiOBe4GagTzXLC+7ElsDXhnPwb4ALgdsL/tLT3ojWhMGhlKfEsK2Xe\nT9HftaN9tAV6AKcDt5nZ5e5+Z1YvTAJ31yNPHsCphC/wa+Xc/h/R9muAU4ACwIAjgR+iZaNSbPf3\naNkLhBNpLeD8aN43gKXY5pXoONvF+H4NjGKclOV2RviBcODWDNbfMVrXgSNyFPvIaH9XxP250yO+\nB/C/6HMwNM06Z0TrvBx3vDl+7fdGr2sZIUFpEc0vALYHfgvsW479fhztd2wG6zYF5gNLgc+i7e5L\ns/68aJ39cvxe7J90jnkR6A3UjZYZsEN0Tn4XOC+D/SXiTHt+ISRtieNu8hkEugBnE5LixHr3xv3Z\nqY4P3WaVjJhZW+CiaPIP7v6wu2/w4FlCCQDASSlu6RwcPV/q7j+6e5G73w5MBjoQTiTJxxoCHARc\n7+6zKuQFZSZR7J/21nNJHs5SI6LJQWZWVgl4olRuIeFEKyKbwcwOJySphcBh7n6buy8FiM5bM939\nX+7+Vpb77Ql0iyYfzmCTa4F2wOXA4myOlWMXRs8fAoe7+5vuvg7C+crdv3D32919L+CBygrK3b90\n9+GEOzuJ455hZmem2UxSUDInmToOqEe4yr2n5EJ3fxr4gnCVN7jE4i2i59kl5icStVaJGWbWFPhn\ntOwfmx118X57WGgU8I2ZrTWzxWb2opkdl2Ldv5iZE26XAhxQor7HgRkcMnGibw0cniYuA4ZGk6Pc\nfUPSsgIzOziq4/KhmX0Xxb7AzJ7MMI6Sxzskeg0z06xTZoV4M9vfzMZGdXzWmtkPZvaSmZ2YZpvt\nzGy4mX1pod7kKjObY2avmtkfzWyL0rYtZX/bW6irOdHMvorq//xooT7nJWZWP5PXZ2bDzOyN6DW4\nmR1ZYv0mZnaFhXpWy6LYvzCzW8ysfZYxd46Osd7MGqVY/lm0/Ecz2+T8bGbfR8v3K+31JM8j3GIF\nGFHiM5zu/z/AzF6LYlgZvZ8DS1m31AYQltQIJ/osX2pm0yzUl1piZs+Y2e7p37Fyuyx6vtfd38nh\nfk+Jnsu88DKzPYBzCRetd+cwhvLoHj0/7+5F6VZ09zWVEE/JY64jlNB9EM36s6Wpgy2bUjInmeoT\nPb/h7j+Vss6E6PmgEvN/iJ63LTF/uxLLIVzJtgUuSHOcrJjZWYS6MUMIJYGrCbd7+wKPm9mIqH5N\nwkpCXZHl0fT6aDrxWFfWMd19JvB2NHlymlUPBDpGf5e80u8OvEy4/dGDUFdnPbAVcAzwqpn9vqxY\ncsmCfwKvE25DtyfUHWpBqF84JvoRr1Viuz2AqcBZhFtcBYTX0onwHlxHeI3ZeBy4gfDZ7ES4Ld8M\n2Au4CXjdzBqX8XruBB4hJD1GuM2TvLwbMAO4hlDHqiGhnmgXQmnHNDPbK9OA3f0rQtWC2sA+JY61\nJeGWO9Hr2LXE8q6Ei4M1wPtlHGo14bOaqHe1jI0/wykb8ZjZXwn1YntHsxoR3s+xZnZ+GccsTR1C\nFYt/EV7fBsLn5Sjgf2a2Zzn3m5KZdQQSye5DOdxvHeCkaHJk8oVXinULgOHR5G/KSqAqUVYXH5XJ\n3QspvoDfmuLPoGRAyVx+6mZmM6IShhUWWjb928w6p9mma/Q8I806icrAvzAzS5o/MXr+l5k1N7Na\nZvYbwo/jPEIFasysB6EC7pPu/nzWryoFM9uHUAm6FuHHf2t3b0FI5i4nqssB/Cmxjbv/092Tbyu/\n7e5tkx5vk5lEcnaUld5CNZHoTXH36SWWrQXGEuokbgk0cPfGhGT3KsKP4nVm9ssM48mFSwl1jb4H\nziHUQ2pK+NEfRCixGBKtk+xfQGNCgtvD3eu6e/No3p7ALRQnz5n6kPA/2h6oH/1fGwBHEyr870m4\nOChNL0JpwBVAS3dvSUgy3gOw0KrvecIPyxOEW0H1o//BdsBooCXwpIUS5Uy9ET0fUGL+/tHzilKW\nJ6bfTdwiK427j44+w4mk7/wSn+G9U2z2S8J34nLC+9GccOGQaID0jzSf43QuJGogRfh/N42mPyH8\nv24uxz7TSby2NcBUM/uNmU2OSoJ/NLO3zezcKDnLxpEU32Uo6xbrRYSLk3vd/YMy1k3lVgutbteZ\n2UIze87MBqUqrc1QohHWYDMbUM59VIYXCY3kQMlcduKutKdH5T0obgDhhC/MD4Qr98S81cDgUrZd\nGq1zQZr9D0jaV5Ok+W2ABdH8DdFxEuudFK1jhMq3K4GOOXzNr0TH+R9QkGJ5onHGCqBpKe/Xa+U8\ndjPCD4oDZ6VY3pCQwDhwUTn2/1dKqTBMKQ0gCKVnDsxMs9+UFeIJicsqQpL5y1K23TfadjFQO2n+\n2mh+yu0q4LO+PaG+1EqgXimvz4Gr0+zj+midx0ndSMcIPz4OXJxFbGdG27xZYv7t0fxro+enSiwf\nE82/KpP/V7QsmwYQTqgPm+pzujhaPrjEsu2j+YVpPoNFwF4plvdKOm77HP7vr4j2+QXhYihxjEQL\n0cT0a0DDLPb7NBk0iCIk/ysIFzwtUvwvMmkA4dF3bXnStBPOZ83K8Z7sQvG5yIGvCHXUzgF2J8W5\nsYz95aQBRCnbzIrWfzhXn4l8eKhkLr8sIJTo7EwoYdiCcKXcj+Kr5EfMbP8U2ybq96SrT7E66e+f\nb2+5+/eEH/lxhJNTLcKV4jHu/mi02lmEk/s17j7XzBpHdZIWRnWh3jezX2XzYs2sJcW3h6/z1LdF\n/kFoLt+Y4i5XcsLdlxF+ACD1rdZjgCaEpOPRFMvL8t/oOaO+rnLgBMIP+xvuPjnVCh4qlH9NKMFI\nvm2aKHXbqkIjLI5jJqH1YCNK3K5MUkj6UqFE/ah/e/QrU+IYTvH/LZvPZqJkbk/buG+tA4haQBPe\nr/1LlHAnSuZez+JY2VgdHXsj7r4aeCma3Lkc+33NU3Tr4+7vEUpyobhRQS4kSg+3J1QFGAd08FDy\n2oxQaryB8H7+K5Mdmlly3deySuVuJ5xPfu9Ro4ssPAkcC7Ry90YeSr23IVQbKCJUYcn6XOHu0wgX\ncp9Gs7YBTiPctZgMLDazu8ysQ7b7rgCJ96xlrFFUM0rm8oi7T3D3q919hhe3ZFrr7uMJ9XdmEuoy\nXZ9uN+U89lfuPtDdW7h7fXffw93/Az/3Q/d3wonmpugH7CnC7ZmvCSfjHYHxZtanlEOk0oPielAp\nfwCjhCuRmFREZezEiX9fMytZZzCR4D0fJbybMLOGUcXx16PK7+sTldgprizcrgLiTiVRx2ufKMlO\n+UiKZ+ukbRO3zUeZ2d/NrFc5bnNtwswOtdAQY3ZUsd6T3p9EglDa+/O5u6fsbzGqctA2mnwyzWu9\nKVpn61T7ScXdPyckMXUJ9dGw0PijGzDD3b8j9MvYkih5MrMdonjWEUqwK8LHXnrl9/nRc4ty7Dfd\nbcbN2W9pEr9rRqjCcZK7z4eQmLr7TcBt0Tqnm1mbDPY5mFD3bz1pkikLHZz3J/z/MmntuhF3v9Dd\nn3L3H5Lmfe3uvyV0Xg5wuJmVrJecyb7fInye+hDqmr5B8S395oRSuulR1ZSqoFy/NflKyZwAPyc1\nf48m94quRJMlOoZsmGY3ycuy6c7jRsIP13nuvp5QN+UQ4Dlgb3cfRig9rE1o6ZqpxGtY5iU6Mi5h\nXon1c2kC8G3097DETDPbiuIuW1Ke9C20lPyIUHqwfxTfWkLl9e8o7upgk1aRFSRRqtaQUIevtEed\npPUSfkuoi9aUUD/xXWC5mb1iZmdbKS1P04kaL7xAKH3pTPh8LKG4kn+i8n9p70+6kTySSxDbUPpr\nTSQh6b4XqbwZPSdK2/YnJB+vRdOvl1ieeH7Pc9QwKIUVaZYljlmeBLyi9lua5O/67aWUyCeS8Dps\nWjcxlUQp7bPunrKLkaixza2EEt9zU5XmbqbbKT5XpR09pzQeuoV6zd3/4O4HED6/vQm3xCEkdWPL\n833MocR3KttSzbymZE6SvRc9G6EYPtmC6DldKVBi2UoyTOYsDIdzCjDa3V+NZie6hrjTo1Zg7v4/\nQoX33S30eZeNelmunzPRD0niRDksadFQQinoEopvl5Z0K+FW0SzCLdkW7t7Y3dt4qNyeaLFnpWyf\na4nzxY3ubhk8Eq8bd19EqJh+KKFUZCqhZOogQrcN080s4xJGC0PB/Ybww3kloUFCPXffwqNK/hSX\nuJb2/pTaGpGNz42NMnit22cae6S0ZO31MpYnbtFK6RYk/f15qhXc/RuKL1DTlqqaWXeKqwykK237\nE6G1/H3A7KiqyM8Pij9TtZPmZ/zdjc6FiVLOkqX85eKhz73/RRfMf41mdyC7agM5E71P20STJbuy\nkjSUzEmy5BNLyavKREvVdHVbEi1eP83kqtRCZ7p3Ea7ck1s/doqevyqxycwSy8uSKHlpkKKkMVmi\nnkjaMVc3Q+IHYLukWxiJxG6Mp2iZGF0ZJ5LaQe7+H990mK8tyxFLoj+wdFfezUqZnxjap2spy9Py\nYEJ0K6kHoaTxHMKQQtuTYf2lyAnR83B3v8bdZ6f4zJXn/UlIHsaoXK+3DIlkbS8zq8emydwkQrJR\nWrInpUtucZ/uPGQZrAOhIRSE88P4NOslzkvnEM5pJR+JVranJM3LtquQTGMuj/uT/t6h1LUq1qEU\n5yVvpltRNqZkTpIl9/f0dYlliVKz3mmK4BNXc69keLyLCH2p/dndFybNT5ywSh4n24GYp1B80ktZ\n187MmhG6ZIBQ8pdz7j6D4lKik6MuWBKdeJZ2pd+GUHIFoRQrlUPKEU4iIWxrG/etl2yPUuYnOl/t\nE3XbsVncfYmH3t+viGZlcrsrIZGAT0m1MKqfmK6rnbLMpPg29rGbsZ/SzCC0Jq9P+AHbBfgkKsHE\nQ59b7wCtLXRi3IGQiGfaLU5CopuHyiq9rQrep/jW7k6pVoj6okvcGi95rkter4DQ1Q6EuweljZda\n4aJuSRLnqjkVcIjkMVbL7Esz16KL+z9Gk3NRMpcVJXN5oqzi/KifrMQX6f3Ej0qSJwn1tZoTujIo\nuf1RFI8xWmZrq6g+2FWEROWOEovnRM+/TFq/gOJbHaWefJNFldsTSegfSumj6Q+EH9SVpL/q3lyJ\npG0gxQN/f+bupXX+mtzn2iYtCKNWZ+eVI47PCHXJCigu+Uve746EftpSGUto8diQMkbnSE72LPQr\nWFriCMUtpLO5HZ4YyLt7Kcuvy2Jfm4hK+RL/swui9yUlC0orzUy3/8SP1RWEc/FrJVZLlMJdGT1P\ncvdsB1lPfI7K0z9cteTuawmNpgDOL+Wzl2hMsIZN3/dkh1Fcwpu2QYO7D013K57QKALg/qT5iTpw\nZZ6jCaNJJG4JP1fGuhsxsz5lfAdh45F7SruArBBRY6i7gZ7RrL/GmThXR0rm8kcnM3vXzE6PrkoB\nMLO6ZnYY4USzA+FK/k8lN45Kzm6JJm+wMARSQbSPI4AHo2WPRs3gy3Izofn+uSkqKCeSqsssDAFV\nQPjB6wB8WKIUryx/jl7T7oTRCTpEMTc2s8soTmCvd/dsO63NxqOEJKoFoaNaSPPjEN1STdSPecjM\ndoWfE6NfEX6Asr7VElWeT9TRu9XM9kkkW9HnYAIbdzGTvO0iikvRzjSzRy2MkEAUW30z621md7Fx\n3a6WwEwz+5OZ7ZxIqpNeyzXRetmMS5voKuNcMzs10TLWzDqZ2UjCbdjNrUD9d8KFRWPgjegz/3OX\nO2bW0cLoIlMoX4X0xHuUKAkteQv19TKWZyJxy/G4bBPOqsyKhzBzS92dxl8JF2g7AqOji0fMrIGZ\nXQJcEK13S2ktmiOJhg/T3T1lKXAO3WGh8/Z9k+9+RJ+zGyg+/77s7i+l3kWp/g18aWZXmVnPpO9L\nLTPb1sz+Ea0D4S5CVmPWlld0fj+LkDyeHs0e7u6VNj5sjeFVoLM7PSr+QahUmtz55BrCbaR1SfNW\nAcPS7KMO4Yowsf5P0TaJ6fdJ6iw4zX76kqbzTMItoVdLxOqEZKhPOV772YTK7okOTJcQblkl9j+S\n1B0Kn8pmdBqcYn9PJR1zA6Hvq3Tr78PGHX2uTJpeTChBK6vD1k069STUT/uhxP89sd/JwMWU0glt\ntP1V0fuYvP2SpPfYgS+T1m9V4rO3Loo/+X/wJdAui/eyXvR5S2xfSHHH1k64IEnZYS5pOtlNcZwu\nhNLM5P/bYjbu+NqBIeX4POxeYh9bpniNyf//w0vZT7pOg7tR/B1fT2gNOSf5M53J+wH8jRTfWTLr\nNLjUjmVL+x9l8N4ld3Sc8ntEKFVLnJ8SnaQnn++eIKlj6xTbNyec4xy4NAff/7SdBie9X4nP2RJC\nCXTyZ2Qi0Lwcx/6gxH4S+19fYv7HZNBpO+XrNPhHQpc8C6PvUMljLwHO2dz3OV8fKpnLH98R+m17\njNDCazWhovtqQmXrfwBd3X1EaTvwUOx9FKGC77sU9+o/lXC7cj93T9cNAVFl79sJX9w/plrHw1mg\nP+H26/eE5O4D4AgvbvGaMQ/1svYgDL/0LaGkZRmhdOcED7dH0rVszJXkkriJnnSLJRUPw4btQ+h4\neCnhxLiQcDtiN8KJN2seOtTdizCiwGLCLddvCCVk+1FGS2R3/yvhlvd9hLplRuj+41tCf3LnsPG4\no0sJn5tbCP/HxYTP3ipCQnYZYYiv5FaIZb2GtYSWsDcQGsoUERK6Fwmfk826zZp0nC8J7/X5hNLQ\npVHshYRuY24ldCtSnk6fp1J8u/gzD/3LJR97LcV9ym2gHKUlHupr9iW8L8sIXa50orjOYY3l7i8Q\nOoy+l1AHqzHhsz2RcEvxeA91E0sziJBQFwKjKjZaAO4kNAJ6m9Ait350/G8I1VyOBw7xTRtCZWJ/\nQov42wm9FiwldFi+nvDe/Bf4NeF7OHfzXkapmlHcpU8jwm/AVMJIFEMJF3N3V9CxazyLsmcRERER\nqYZUMiciIiJSjSmZExEREanGlMyJiIiIVGNK5kRERESqMSVzIiIiItVY7bgDqCytWrXybbbZJu4w\nRERERMo0efLkxe6eblzxn+VNMrfNNtswadKkuMMQERERKZOZZTR0Jeg2q4iIiEi1pmROREREpBpT\nMiciIiJSjSmZExEREanGlMyJiIiIVGNK5kRERESqsViTOTM7zMw+N7OZZvbHNOsdb2ZuZj2T5v0p\n2u5zMzu0ciIWERERqVpi62fOzAqAO4BfAfOAD8zsGXf/pMR6TYALgfeS5nUFBgHdgHbAy2a2g7tv\nqKz4RURERKqCOEvm9gRmuvtsd18HjAEGpFjvGuAG4KekeQOAMe6+1t2/AmZG+xMRERHJK3GOANEe\n+CZpeh7QK3kFM+sBbO3uz5rZ70ps+26JbduXPICZnQWcBdCxY8cchS0i+W7lypWsXLmSn376CXfH\nzGjQoAFNmjShYcOGcYcnInkmzmTOUszznxea1QL+DZya7bY/z3C/B7gHoGfPnpssFxHJRFFREXPn\nzuXJRx/lh2++oWDNGuq7U3fDBmqZUQSsq1WL1WZYo0Zsue22HDtoEFtttRVmqU5XIiK5E2cyNw/Y\nOmm6A7AgaboJsDPwWnQybAs8Y2b9M9hWRGSzbdiwga9mzeK5kSN5c+JEBnbvzt7Nm9Ngiy1K3Wb1\n+vXM+uQTzh84kH4DBnDw8cfTsVMnatVS5wEiUjHMPZ4CKzOrDXwBHAzMBz4ABrv7jFLWfw34nbtP\nMrNuwGhCPbl2wCtAl3QNIHr27OmTJk3K7YsQkRpr3rx5TH7hBcaPHUu3Vq244MADsyplK9ywgetf\nfJHvCgvpd9JJ7P6rX9GmTZsKjFhEahIzm+zuPcteM8aSOXcvNLPzgReBAuABd59hZlcDk9z9mTTb\nzjCzx4BPgELgPLVkFZFcWLt2LVPfeYd3xo7l008+4fLDD6djy5ZZ76d2QQFXHHEEn377LTfedRdf\nTZ5MrxNOYJc99qB27ThviohITRNbyVxlU8mciJRlyZIlvPH447w4diy9tt6aU/beOyd13jYUFXH7\nq68ya9kyDhs6lP3696dp06Y5iFhEaqpqUTInIlKVfD1nDqNuvJGvP/6Yq/r1o13z5jnbd0GtWlx0\n8MHM/P57/nbXXXzx8ccMuvhi2rZtm7NjiEj+Uo1cEcl7k957jz+dcQZbrVrF3YMH5zSRS7Z9mzY8\nMGwYRbNn84df/5rPP/20Qo4jIvlFyZyI5LUxo0Zx/e9+x3WHHMJp++xT4V2J1KpVi0sPOYTf9+rF\n7884gwkvvlihxxORmk+3WUUkb7360ks8OXw4IwcNon6dOpV67G5bbcUjAwcy7Oqrad26NT12371S\njy8iNYdK5kQkL3380UfcfOWVDD/22EpP5BKaNWjA7f37c/VFFzHnq69iiUFEqj8lcyKSd76eM4e/\n//a3XHfYYbSIefitji1acPFee3HtxRfz3XffxRqLiFRPSuZEJK8sXryYW6+4guO7dKHrVlvFHQ4A\nB3TpQo/GjRn+t7+xfPnyuMMRkWpGyZyI5I1Vq1Yx6uababpiBcf26BF3OBs594AD+OHTT3nyvvtY\nu3Zt3OGISDWiZE5E8kJhYSETxo1j6muv8efDD487nJRuPPZYXhw3jjdfeIF86dBdRDafkjkRyQsf\nvvMOjw4fzi0nnFBlB72vW7s2Nx59NA/86198Mm1a3OGISDVRNc9oIiI59M3cudx17bX8uW9fmjZo\nEHc4aXVo0YIz9tiDu66+mkWLFsUdjohUA0rmRKRGW7lyJXf+7W8c3L493du3jzucjBy0445sU6sW\nD950k+rPiUiZlMyJSI1VVFTEuAcfZN3cuQzt1SvucLLy20MO4fO33+bF//wn7lBEpIpTMiciNdaH\nH3zAs6NH848BA+IOJWtmxi3HHcf9t9zCF59/Hnc4IlKFKZkTkRpp6dKlXPP733Pz0UdTu6Ag7nDK\npXH9+lzTty9/vvhiVq9eHXc4IlJFKZkTkRqnqKiIy3/7W87abTe2btEi7nA2yy7t2nFo+/Zc/9e/\nxh2KiFRRSuZEpMZ5beJEbOFC+nXrFncoOXHqHnswe9Ikpk+fHncoIlIFKZkTkRpl1apV3H799fzl\nkEPiDiVnaplx5UEH8Y/LL2fdunVxhyMiVYySORGpUUbeey/7tGpF68aN4w4lp3Zo3Zp2RUWMV+tW\nESlByZyI1Bjz5s3jhXHjuPiAA+IOpUJc2bcvj9x5J0uWLIk7FBGpQpTMiUiNUFhYyG3XXssZv/xl\ntW29WpbG9evTt2NHHrztNo3dKiI/UzInIjXC9KlTmT9jBv123jnuUCrU2fvuyzsTJjB71qy4QxGR\nKkLJnIhUe6tXr+b2a6/lsoMPjjuUCmdmnLvXXtxx7bWsX78+7nBEpAqINZkzs8PM7HMzm2lmf0yx\n/Bwzm25mU83sf2bWNZq/jZmtieZPNbO7Kz96EakqXn/hBRqvWkXXrbaKO5RKcdCOO7Jk9mwmv/de\n3KGISBUQWzJnZgXAHcDhQFfgpESylmS0u3d3992AG4CbkpbNcvfdosc5lRO1iFQ1S5Ys4eE77uDK\nww+PO5RKdXnfvtx9ww2sXLky7lBEJGZxlsztCcx099nuvg4YA2w0gKK7L0+abASoxq+IbOTJESPY\ntXlztmjUKO5QKlWX1q3ZYt06Xn3++bhDEZGYxZnMtQe+SZqeF83biJmdZ2azCCVzFyYt6mxmU8zs\ndTPrXbGhikhVNG/ePJ4fN47f5UFduVT+fNhhjLjrLn744Ye4QxGRGMWZzFmKeZuUvLn7He6+HfAH\n4Ipo9rdAR3fvAVwKjDazppscwOwsM5tkZpMWLVqUw9BFJG5FRUU8eMstnNC1K3Vq1447nFg0b9iQ\nPVu14vGHH447FBGJUZzJ3Dxg66TpDsCCNOuPAY4GcPe17v5D9PdkYBawQ8kN3P0ed+/p7j1bt26d\ns8BFJH6zZs7k43feYVDPnnGHEquL+vThxSef5Ntvv407FBGJSZzJ3AdAFzPrbGZ1gUHAM8krmFmX\npMl+wJfR/NZRAwrMbFugCzC7UqIWkdgVFhZyy9/+xkW9VcOiTkEBg3bembv/+U91JCySp2JL5ty9\nEDgfeBH4FHjM3WeY2dVm1j9a7Xwzm2FmUwm3U0+J5u8PTDOzj4DHgXPcXePbiOSJqR9+yKp589in\nc+e4Q6kSBu6+O5++/z6zZ+tAnJYNAAAgAElEQVSaViQfWb5cyfXs2dMnTZoUdxgispkKCws59bjj\n+GuvXmzXqlXc4VQZ73z1FSMXLOC2Bx+kVi31By9S3ZnZZHfPqB6JvvEiUq28PGECW27YoESuhL07\nd2b1/PlMnTIl7lBEpJIpmRORamP9+vUM//e/+VOedkVSlsv69OFf11xDUVFR3KGISCXKOJkzswYV\nGYiISFmefvJJdm/ZklZ51kFwprq0bk3LwkLeefvtuEMRkUqUTcnct2Z2l5n9ssKiEREpxfr163n0\n/vu5YJ994g6lSrt0v/2461//UumcSB7JJpl7GzgDeD8a3P58M2teQXGJiGzklZdeokuDBjRvoJsE\n6XRu2ZKGq1fz0dSpcYciIpUk42TO3Y8AOgFXEsZJvRVYYGajzKxPBcUnIkJhYSEP3n47l+y/f9yh\nVAsX7bsvd9xwg0rnRPJEVg0g3H2Bu1/r7l2Ag4EnCaMyvGxms8zsMjNrVxGBikj+eu+dd2jtzpZN\nmsQdSrXQrW1b1n3/PTNnzow7FBGpBOVuzerur7r7UKAdMAroDFwDzDGzp8xszxzFKCJ5rLCwkOE3\n3cRvVSqXlXN69eKOf/xDo0KI5IFyJ3Nm1srMLgHeAoYCq4AHgXuBg4C3zezMnEQpInlr+vTp1F2x\ngs5bbBF3KNXKPp07892sWcydOzfuUESkgmWVzFlwmJmNA+YB/wLWAucC7dz9DHc/D+gIvAb8Ocfx\nikgeKSoqYvg//8kF++4bdyjV0sm77sq9N98cdxgiUsGy6WfuauBr4DngUOBhYA93/6W73+3uKxLr\nuvuyaHn7HMcrInlk1qxZrJg/n13b61RSHod37cpnkyfz3XffxR2KiFSgbErmrgC+A84BtnL3s919\ncpr1PwSu3pzgRCR/uTv33HQTZ/TMaGhCScHM6N+lC6PuvTfuUESkAmWTzO3u7nu4+73uvqqsld19\nhrv/dTNiE5E8tmDBAr6eMYM+O+wQdyjV2pA99uB/L73Ejz/+GHcoIlJBsknmbjKzUgdENLM+ZjYx\nBzGJiPDQnXdyQrducYdR7RXUqsV+W23F02PHxh2KiFSQbJK5A4Et0yxvAxywWdGIiAA//PADH775\nJsfuumvcodQI5/buzTNjx7Jy5cq4QxGRClDurklSaE5o2SoislkeHzWKgzt2pKBWLk9R+at+nTp0\nbdKEiRMmxB2KiFSA2ukWmtkuwG5Js3qbWaptWhK6J/kkh7GJSJ56ZcIE7jrkkLjDqFFO23tv/vrY\nY/Q/9ti4QxGRHEubzAHHAFdFfztwdvRIZQVwYY7iEpE89fHHH7N1u3bUVqlcTjWsW5eGDRqwcOFC\n2rZtG3c4IpJDZZ0tHwL6EEZ0MODv0XTy40CgJ7Clu79QUYGKSH4YNWoUB6uT4ApxZN++3H///XGH\nISI5lrZkzt2/JnQUjJmdBrzh7l9VRmAikn+++eYb2rRpQ906deIOpUZq1rQp69evZ/ny5TRt2jTu\ncEQkRzK+j+HuDyuRE5GK9MADD/DrX/867jBqtNNOO40HH3ww7jBEJIdKLZkzs5OjP0e4uydNp+Xu\nj+QkMhHJK0uWLKGgoIBmzZrFHUqN1qlTJ7799lvWrl1LvXr14g5HRHIg3W3WhwiNHsYA65KmLc02\nDiiZE5GsqVSu8gwePJjRo0dz2mmnxR2KiORAumSuD4C7r0ueFhHJtTVr1rB06VLatWsXdyh5YZdd\nduGRRx6hqKiIWmo1LFLtlZrMufvr6aZzwcwOA24BCoD73P36EsvPAc4DNgArgbPc/ZNo2Z+A06Nl\nF7r7i7mOT0Qqx8iRIxk2bFjcYeSVI488kueee46jjjoq7lBEZDPl5JLMzLKueGFmBcAdwOFAV+Ak\nM+taYrXR7t7d3XcDbgBuirbtCgwCugGHAXdG+xORasbd+eKLL9hpp53iDiWvHHDAAbzxxhtxhyEi\nOZBxMmdmh5vZX0rMO9fMlgOrzGy0mWXTn8CewEx3nx3dyh0DDEhewd2XJ002ItTJI1pvjLuvjVrY\nzoz2JyLVzJtvvsn+++8fdxh5x8zo0qULX3zxRdyhiMhmyqZk7v+Any+dzewXhFukC4CXgBMJt0Qz\n1R74Jml6XjRvI2Z2npnNIpTMXZjltmeZ2SQzm7Ro0aIsQhORyjJ+/HiOOOKIuMPIS4MHD+bRRx+N\nOwwR2UzZJHO/ACYlTZ8IrAH2dPfDgbHAKVnsL1WrWN9khvsd7r4d8Afgiiy3vcfde7p7z9atW2cR\nmohUhgULFtCmTRsKClRLIg6NGzfG3Vm1alXcoYjIZsgmmWsBLE6aPgSYmHQr9DWgcxb7mwdsnTTd\ngVDKV5oxwNHl3FZEqqBHHnmEk0/OqAtLqSAnnXQSo0ePjjsMEdkM2SRzi4FOAGbWBNgD+F/S8jqE\nVqmZ+gDoYmadzawuoUHDM8krmFmXpMl+wJfR388Ag8ysnpl1BroA72dxbBGJ2fr161m2bBmtWrWK\nO5S8tuOOO/LFF1/gvsnNDRGpJtKOzVrCO8A5ZjaD0AK1NjA+afn2wLeZ7szdC83sfOBFQhL4gLvP\nMLOrgUnu/gxwvpkdAqwHlhLdxo3Wewz4BCgEznP3DVm8FhGJ2VNPPcUxxxwTdxgC7Lvvvrz11lvs\nt99+cYciIuWQTTJ3FfAq8Fg0/XBSn28GHBMtz5i7j2fjhBB3vzLp74vSbHstcG02xxORquODDz5g\n4MCBcYchhD7nrrjiCiVzItVUxsmcu38StWDdF1jm7skdFDUH/k2oNyciktb06dPp1q1b3GFIpHbt\n2rRq1YqFCxfStm3buMMRkSxl1Wmwuy9x9/+WSORw96Xufou7f5Tb8ESkJnrsscc48cQT4w5Dkpx8\n8sk88oiG1hapjrK5zfozM2sIbEGKLkLcfe7mBiUiNdeyZcuoV68eDRo0iDsUSdKmTRuWLFlCYWEh\ntWuX66dBRGKSzQgQtczsj2Y2H1gBzAG+SvEQESnVqFGjGDJkSNxhSAoDBgzg6aefjjsMEclSNpdf\n1wO/A2YATwA/VEhEIlJjuTtz5syhc+dsuqSUyrLXXnvxf//3fxx33HFxhyIiWcgmmRsKvODuGndH\nRMrllVde4aCDDoo7DCmFmdG1a1dmzJihBioi1Ui2I0Co/F1Eym3ChAn07ds37jAkjUGDBjFmzJi4\nwxCRLGSTzE0HtqqoQESkZps7dy4dOnSgVq2sGtFLJWvYsCF16tRh+fLlZa8sIlVCNmfVvxJGgNi6\nzDVFREoYMWIEw4YNizsMycCQIUMYNWpU3GGISIayqTP3S+Br4BMze4rQcrXkEFru7tfkKjgRqRnW\nrl3L6tWradGiRdyhSAa22247Zs+ejbsTBvgRkaosm2TuL0l/Dy1lHQeUzInIRh5//HFOOOGEuMOQ\nLBx44IG89tpr9OnTJ+5QRKQM2dxm7ZzBY9tcBygi1d9HH33EbrvtFncYkoXDDjuMF154Ie4wRCQD\n2YzN+nVFBiIiNdOUKVOUyFVDBQUFtG3blnnz5tGhQ4e4wxGRNMrVrMzMtjezfc2sWa4DEpGa5fHH\nH1cntNXUySefzIgRI+IOQ0TKkFUyZ2ZHmtks4HPgDUKjCMysjZnNNLPjKyBGEammlixZQqNGjahX\nr17coUg5bLHFFixfvpx169bFHYqIpJHN2KwHAk8BSwjdlPzcxMndvwdmAYNyHJ+IVGPqjqT6O+64\n43jiiSfiDkNE0simZO5K4COgF3BHiuXvALvnIigRqf6KioqYP38+W2+trimrs549ezJ58uS4wxCR\nNLJJ5noCo9y9qJTl84C2mx+SiNQEEydO5OCDD447DMmBxHitIlI1ZZPMFQBr0yxvBahihYgA8PLL\nL/OrX/0q7jAkB0488UQee+yxuMMQkVJkk8x9CvROs/xIwm1YEclzCxcupE2bNhqHtYZo1KgR7s7q\n1avjDkVEUsjmTHs/cLyZnZ60nZtZQzO7FdgbuCfXAYpI9TNy5EiGDBkSdxiSQwMHDlTpnEgVlXEy\n5+53AWOBe4EvCUN3PQosA84HHnJ3jcwskueKiopYvHgxW265ZdyhSA7tvPPOqjcnUkVldQ/E3YcC\nxwGvAJ8RuikZD5zg7qfnPjwRqW4mTJhA37594w5DKsAuu+zCtGnT4g5DRErIukKLuz/l7se5ezd3\n7+ruA9y9XJ0QmdlhZvZ51OHwH1Msv9TMPjGzaWb2ipl1Slq2wcymRo9nynN8Ecm9V199VYOz11DH\nH38848aNizsMESkhttrJZlZA6K/ucKArcJKZdS2x2hSgp7vvAjwO3JC0bI277xY9+ldK0CKS1vz5\n89lqq60ws7JXlmqnQYMGFBQUsHLlyrhDEZEkGSVzZtbMzC4zs7fMbJGZrY2e/2dmfzSzpuU49p7A\nTHef7e7rgDHAgOQV3P1Vd080n3oX0GjPIlXYyJEjGTp0aNxhSAUaNGgQY8eOjTsMEUlSZjJnZrsA\nM4BrCC1W6wLfR8/7AH8HPk5RqlaW9sA3SdPzonmlOR14Pmm6vplNMrN3zezoLI8tIjlWWFjI0qVL\nadWqVdyhSAXaaaed+Oyzz+IOQ0SSpE3mzKw+8ATQmpC0dXb3Zu6+tbs3AzpH87cEnjSzbEbTTnUf\nxkuJYyhhBIobk2Z3dPeewGDgZjPbLsV2Z0UJ36RFixZlEZqIZOv555/niCOOiDsMqQS77767hvgS\nqULKKpkbBGwHDHb3P7v718kL3f1rd78CGArsEK2fqXlA8qCNHYAFJVcys0OAy4H+7v7zCBTuviB6\nng28BvQoua273+PuPd29Z+vWrbMITUSy9eabb9K7d7p+xaWmOPbYY3nqqafiDkNEImUlc/2B98tq\nreru44D3KVHnrQwfAF3MrLOZ1SUkghu1SjWzHsBwQiL3fdL8FolSQDNrBewLfJLFsUUkh77++ms6\nduyohg95ol69etStW5fly5fHHYqIUHYytyswIcN9TYjWz4i7FxI6G36RMFTYY+4+w8yuNrNE69Qb\ngcbAuBJdkPwCmGRmHwGvAte7u5I5kZiMGjVKIz7kmcGDBzN69Oi4wxARoHYZy1sDczPc19xo/Yy5\n+3hCp8PJ865M+vuQUrZ7G+iezbFEpGKsX7+eFStW0KJFi7hDkUq0/fbbM3z4cNxdJbIiMSurZK4R\nkOnIymui9UUkj/z3v/+lf3919ZiPevXqxfvvvx93GCJ5r6xkTpdbIpLWO++8w1577RV3GBKDAQMG\n8PTTT8cdhkjeK+s2K8BvzSyTVqrp+ogTkRpo1qxZbLvttrrNlqfq1KlDo0aN+PHHH2nevHnc4Yjk\nrUySuR6k6PajFCn7iRORmunRRx/lggsuiDsMidGQIUMYNWoU5513XtyhiOSttMmcu8c2dquIVG3r\n1q1jzZo1NGvWLO5QJEbbbLMNc+bMUUMIkRgpWRORcnnqqac45phj4g5DqoD99tuPt956K+4wRPKW\nkjkRKZfJkyfTs2fPuMOQKqBfv34899xzcYchkreUzIlI1j7//HO6dOkSdxhSRdSuXZumTZvyww8/\nxB2KSF5SMiciWRszZgyDBmUzFLPUdEOHDmXUqFFxhyGSl5TMiUhWfvrpJwoLC2nSpEncoUgVsvXW\nWzNv3jzc1amBSGVTMiciWRk3bhzHH3983GFIFXTggQfy6quvxh2GSN5RMiciWZk2bRq77rpr3GFI\nFXTooYfy4osvxh2GSN7JOJkzs5fM7EQzq1uRAYlI1TV16lQlclKqgoICttxySxYsWBB3KCJ5JZuS\nuV8Co4EFZnazmXWvoJhEpIp6/PHHdYtV0ho2bBgjRoyIOwyRvJJNMtcWGAJMAS4ApprZe2Z2ppk1\nrpDoRKTKWL58OXXr1qV+/fpxhyJVWOvWrVm6dCmFhYVxhyKSNzJO5tx9nbuPcfdfAdsCfwO2BIYD\n35rZ/Wa2bwXFKSIxGzVqFEOGDIk7DKkGjjrqKJ599tm4wxDJG+VqAOHuX7v7VUBn4DDgVeBU4A0z\n+8TMLjKzRrkLU0Ti5O7Mnj2b7bbbLu5QpBrYZ599NLyXSCXa3NasuwH9gd6AAbOAIuDfwEwz22cz\n9y8iVcCbb75J79694w5DqgkzY/vtt+fLL7+MOxSRvJB1Mmdmzc3sPDP7EJgEnAG8CBzi7ju4+87A\nIcBq4I6cRisisRg/fjz9+vWLOwypRgYPHszo0aPjDkMkL2TTNclBZjYKWADcBjQEfg+0d/dB7j4x\nsW709/VAtxzHKyKV7LvvvmOLLbagoKAg7lCkGmnSpAmFhYWsWbMm7lBEarxsSuZeBo4FngL6uPtO\n7v4vdy9tZOWZgCpNiFRzI0aMYNiwYXGHIdXQwIEDeeyxx+IOQ6TGyyaZ+y2hFG6Iu79e1sru/qq7\n9yl/aCIStw0bNrBo0SLatm0bdyhSDXXv3p2PP/447jBEarxskrkmQLvSFppZNzO7cvNDEpGq4vnn\nn+eII46IOwypxnr06MGUKVPiDkOkRssmmbsK2CXN8p2jdUSkhnjjjTfYf//94w5DqrHjjjuOJ554\nIu4wRGq0bJI5K2N5fSCrLr/N7DAz+9zMZprZH1MsvzTqt26amb1iZp2Slp1iZl9Gj1OyOa6IlO2r\nr76iU6dOmJX11RcpXb169ahXrx7Lli2LOxSRGittMmdmTc2so5l1jGZtkZgu8diNMNTXN5ke2MwK\nCF2XHA50BU4ys64lVpsC9HT3XYDHgRuibVsSSgF7AXsCV5lZi0yPLSJlGzlyJEOHDo07DKkBhg4d\nysiRI+MOQ6TGKqtk7hLgq+jhwM1J08mPyYS+5e7O4th7AjPdfba7rwPGAAOSV4gaUayOJt8FOkR/\nHwq85O5L3H0p8BJhJAoRyYG1a9fy008/0axZs7hDkRqgc+fOzJkzB3ePOxSRGql2Gctfi54NuJLQ\nLcm0Eus4sBJ4193fzuLY7dm4JG8eoaStNKcDz6fZtn0WxxaRNB5//HGOP/74uMOQGuSAAw7g9ddf\n58ADD4w7FJEaJ20yF3VB8jpAVF/tbnd/L0fHTlURJ+Vlm5kNBXoCB2SzrZmdBZwF0LFjx002EJHU\npk6dypAhQ+IOQ2qQww8/nMsuu0zJnEgFyLgBhLuflsNEDkJp2tZJ0x0Io0tsxMwOAS4H+rv72my2\ndfd73L2nu/ds3bp1zgIXqcmmTZtG9+7d4w5DapiCggJat27NwoUL4w5FpMYpNZkr0fCBUho+bPLI\n4tgfAF3MrLOZ1QUGAc+UiKEHMJyQyH2ftOhFoK+ZtYgaPvSN5onIZho3bhwDBw6MOwypgU4++WRG\njBgRdxgiNU6626xzgCIzaxg1UJhDKbdBS8hoAEd3LzSz8wlJWAHwgLvPMLOrgUnu/gxwI9AYGBd1\njzDX3fu7+xIzu4aQEAJc7e5LMjmuiJRuxYoV1K5dm/r168cditRAbdq0YfHixWzYsEFj/YrkULpk\n7mpC8lZYYjpn3H08ML7EvCuT/j4kzbYPAA/kMh6RfDd69GgGDx4cdxhSg/Xr14/nnnuO/v37xx2K\nSI1RajLn7n9JNy0iNYu7M3PmTM4+++y4Q5EarHfv3vz+979XMieSQ9mMACEiNdhbb73FvvvuG3cY\nUsOZGdtuuy2zZs2KOxSRGkPJnIgA8Mwzz3DkkUfGHYbkgSFDhmhECJEcKvU2q5kVkX0dOXf3sjoi\nFpEqZu7cubRr147atfX1lYrXtGlT3J3ly5fTtGnTuMMRqfbSnbkfIccNHkSkanr44Ye54IIL4g5D\n8sgpp5zCiBEjOO+88+IORaTaS9cA4tRKjENEYrJy5UrWr19P8+bN4w5F8kjnzp35+uuv1U2JSA6o\nzpxInhs5ciTDhg2LOwzJQ0cddRTPPvts3GGIVHtK5kTyWFFRETNnzqRLly5xhyJ5aL/99uONN96I\nOwyRai9dA4ivgCJgJ3dfb2azM9ifu/t2OYtORCrU888/zxFHHBF3GJKnzIzddtuNKVOm0KNHj7jD\nEam20pXMfQ3MpbgRxNxoXrrH3AqLVERybuLEifTp0yfuMCSPnXjiiTz22GNxhyFSraVrAHFgumkR\nqd6mT59O9+7dicY9FolF3bp1admyJQsXLqRt27ZxhyNSLanOnEieGjNmDIMGDYo7DBFOPfVUHnro\nobjDEKm2su4h1MzqAQcC20azZgOvu/tPOYxLRCrQ999/T9OmTalfv37coYjQunVrVqxYwU8//aTP\npEg5ZFUyZ2YnA/OB8cAd0WM8MN/MTs15dCJSIR566CFOPfXUuMMQ+dngwYMZPXp03GGIVEsZJ3Nm\ndiLwELASuBw4GjgGuCKad3+0johUYWvXruXHH39kyy23jDsUkZ9169aNTz75BHcNPCSSrWxK5i4D\nPgN2cffr3f0Zd3/a3a8DdgG+JCR5IlKFjR07lhNP1HWXVD0HH3wwEydOjDsMkWonm2RuR+BBd19e\ncoG7LwMeBNTzqEgV5u5MmzaNXXfdNe5QRDZx6KGH8sILL8Qdhki1k00ytxBI14dBEfDd5oUjIhXp\njTfe4IADDog7DJGUatWqxfbbb88XX3wRdygi1Uo2ydxDwKlm1rjkAjNrCvyaUDonIlXUs88+S79+\n/eIOQ6RUQ4cOZeTIkXGHIVKtpBvOa/8Ss94AjgSmm9mdhPpzDnQFfgMsBt6soDhFZDPNmjWLzp07\nU6uWupeUqqtRo0bUrVuXpUuX0qJFi7jDEakW0vUz9xrFQ3klJG6z/iNpWWJeJ+AloCBXwYlI7owY\nMYLf/e53cYchUqZEJ8KXXHJJ3KGIVAvpkrnTKi0KEalQy5Yto1atWjRuvEktCZEqp0OHDixcuJDC\nwkJq1866b3uRvJNubNaHKzMQEak4Dz/8MKecckrcYYhk7LjjjuPJJ59k4MCBcYciUuXFWnnGzA4z\ns8/NbKaZ/THF8v3N7EMzKzSz40ss22BmU6PHM5UXtUj1smHDBubPn0+nTp3iDkUkY3vuuSfvv/9+\n3GGIVAvlGZt1S6An0IIUyaC7P5LhfgoIw4H9CpgHfGBmz7j7J0mrzQVOBVJV9Fnj7rtlF71I/nn6\n6acZMGBA3GGIZK1Xr16899579OrVK+5QRKq0jJM5M6tFSL7OIH2JXkbJHLAnMNPdZ0f7HwMMAH5O\n5tx9TrSsKNM4RWRjb731Fv/85z/jDkMka8cccwyXX365kjmRMmRzm/V3wNnAo8AphFasfwTOIwzl\nNYlQypap9sA3SdPzonmZqm9mk8zsXTM7OovtRPLG66+/Tu/evTFL19+3SNVUu3ZtOnfuzGeffRZ3\nKCJVWjbJ3CnAi+5+MvB8NG+yu98N/BJoFT1nKtWvSzYjLHd0957AYOBmM9tukwOYnRUlfJMWLVqU\nxa5Faoann36a/v37xx2GSLkluikRkdJlk8xtS3ESl7jtWQfA3VcRRn84I4v9zQO2TpruACzIdGN3\nXxA9zyb0idcjxTr3uHtPd+/ZunXrLEITqf7efvtt9t57b3USLNVa/fr16dChA7NmzYo7FJEqK5uz\n/BpgffT3SkIpWpuk5QvZODkrywdAFzPrbGZ1gUFARq1SzayFmdWL/m4F7EtSXTsRgSeeeILjjjsu\n7jBENtuvf/1rHnjggbjDEKmysknmvga2A3D39cBM4LCk5YcA32W6M3cvBM4HXgQ+BR5z9xlmdrWZ\n9Qcwsz3MbB5wAjDczGZEm/8CmGRmHwGvAteXaAUrktfef/99dt99d5XKSY3QsGFDWrVqxZw5c+IO\nRaRKyuZMPxE4Jml6BHCSmb1qZq8REq7Hsjm4u4939x3cfTt3vzaad6W7PxP9/YG7d3D3Ru6+hbt3\ni+a/7e7d3X3X6Pn+bI4rUtM99thjnHjiiXGHIZIzZ555Jvffr1O9SCrZ9DP3T2CCmdVz97XAdYTb\nrEOBDcA9wFW5D1FEsjFlyhS6d++uYZCkRmncuDHNmjVj3rx5dOjQIe5wRKqUjEvm3P1bd38xSuRw\n9w3ufqG7t3T31u7+G3f/qeJCFZFMjB49msGDB8cdhkjOnXnmmdx7771xhyFS5ahCjUgN8vHHH7Pj\njjtSp06duEMRyblmzZrRsGFDFi5cGHcoIlVK1smcmQ00s0fN7L3o8aiZaSRkkSpgxIgRDBs2LO4w\nRCrMWWedxT333BN3GCJVSjbDeTUEngYOInT4+2P0vAcw0MzOBvpHfc6JSCX77LPP6Ny5M/Xq1Ys7\nFJEK06JFCwoKCli0aBHqP1QkyKZk7u/AwcBtQLuorlwLoF00rw9wbe5DFJFMPPTQQ5x66qlxhyFS\n4c4++2yVzokkySaZOxEY5+4Xu/vPFRbcfaG7Xww8Ea0jIpVs5syZtG/fnvr168cdikiFa9WqFUVF\nRSxZsiTuUESqhGySuaaEDnpLMzFaR0Qq2QMPPMDpp58edxgilebMM89U6ZxIJJtkbhrQJc3yLsD0\nzQtHRLI1Z84cWrduTcOGDeMORaTStG3blp9++olly5bFHYpI7LJJ5q4AzjSzo0ouMLMBwBnAZbkK\nTEQyc//993PGGWfEHYZIpVO/cyJBqa1ZzSzVqMZfAf8xs88J46k60BXYkVAqN4Rwu1VEKsG8efNo\n1qwZTZo0iTsUkUrXvn17li1bxooVK/QdkLyWrmuSU9Ms2yl6JNsF6A6o4o5IJbn33nu59NJL4w5D\nJDZnnnkm9913H5dcckncoYjEptRkzt01OoRIFbZw4UIaNGhAs2bN4g5FJDYdO3Zk8eLFrFq1ikaN\nGsUdjkgslLCJVFPDhw/nrLPOijsMkdidfvrpPPBAqppBIvkh4xEgEszMgB7AttGs2cAUd/dcBiYi\npfv++++pXbs2LVu2jDsUkdhtu+22LFiwgNWrV6tVt+SlrErmzOwwYBbwATA2enwAzDSzQ3Mfnoik\ncuutt3LuuefGHYZIlXHOOedw5513xh2GSCyyGZt1X+AZYBVwK/BxtKgbobHEM2bWx93fznWQIlJs\n+vTpdOjQgRYtWsQdikdZ878AACAASURBVEiV0alTJ9atW8eCBQto165d3OGIVKpsSuauBBYCXd39\nEne/P3pcSkjovovWEZEK4u7cf//9Gu1BJIULLriA2267Le4wRCpdNslcL+Aed/+25IJo3r3AXrkK\nTEQ2NX78ePr27UudOnXiDkWkymnSpAldunThww8/jDsUkUqVTTJXF1iRZvnyaB0RqQDr16/npZde\n4vDDD487FJEq65RTTuHhhx9GbfIkn2STzH0KDDKzTerZRfNOjNYRkQpw7733cuaZZxIalItIKgUF\nBRx99NE8+eSTcYciUmmySebuItxqfcXM+plZ5+hxJPBKtExNiUQqwJIlS/j222/p1q1b3KGIVHl9\n+vTh7bffZu3atXGHIlIpMk7m3P0+4EZgP0Kr1pnR4+lo3o3ufn9FBCmS72699VYuvPDCuMMQqTbO\nOecc7r777rjDEKkUWXUa7O5/MLP7gQFAZ8AI/c494+5fVEB8Innv888/p0WLFrRu3TruUCrdI++8\nw8PvvMMGdx457TSmz5/PjRMmAPD5woXcPWQIA3bbDYCbXnqJJ6dM4X+//z1zFi+m1/XX84uttqJu\nQQETLr44zpchMejSpQs//vgj33//PW3atIk7HJEKlVEyZ2b1CLdRv42SthtzcfCoE+JbgALgPne/\nvsTy/YGbgV2AQe7+eNKyU4Arosm/ufvDuYhJpKoZPnw41113XdxhVLoFP/7ImzNn8sqll/48r2PL\nlvTr3h2AXtddx8E77QTA2vXr+WjevI22/9UvfsFIdeGS1y688EJuuukmrrnmmrhDEalQmd5m3UCo\nF5ezZnRmVgDcEe2zK3CSmXUtsdpcQofEo0ts2xK4ipBg7glcZWbqQVVqnJdffpnevXtTr169uEOp\ndK989hkbioo4+KabuGjsWIqKin5eNmvRIrZq1ozG9esDcN///scpe++90favfvEFvW+8kVsnTqzU\nuKXqaNGiBe3bt+fjjz8ue2WRaiyjZM7dCwkdBueyGd2ewEx3n+3u64AxhNu3yced4+7TgKIS2x4K\nvOTuS9x9KfAScFgOYxOJ3YYNG3jmmWc4+uij4w4lFotWrOCn9et55dJLqV+7Nk9/9NHPy5748EOO\n6dEDgPUbNvD6l19yUFRKB7BVs2Z8cfXVvHrppUz45BOmz59f6fFL1XD66adz3333qasSqdGyac06\nDhhoZlmN55pGe+CbpOl50byK3lakWnjwwQc57bTTamRXJN9//z3r1q1Lu07T+vU5YIcdADhop534\n5Nvi/sr/O20a/XfZBYAR777L4D333GjbenXq0KhePWoXFNCve3clc3msTp06HHrooYwfPz7uUEQq\nTDaJ2X1AQ/6/vTuPq6rO/zj++rCLBqISIq6YG6ZSkaSjRs2vcrcxzaaaJrOsGU0SHdQ00lLDQQlN\nmxlbnLFytEkda8ot13HSRtM0FTVcUXFfAFeW7+8PLgwgCCjcA/d+no/HeTzuvWe57y8K93PPOd/v\nF1aKSC8RaSkiDQsvZTheUZ9Qpf3qVKp9RWSwiGwRkS2nT58uQzSlrJWamsqBAwe4x3b2yZG8/vrr\nBAQEEBISwrlz54rdrn2TJuyw3Qf3Y3IywXXqADn30nl7eOBXvTqQ0xHiT+vW0XX6dHalpPDe6tWk\nXb2ad5z/JCXl7aucU7du3fj222/JyMiwOopSFaIsxdxOcjoiPAT8E9gFHCxiKa2jQIN8z+sDx8tz\nX2PMbGNMmDEmzBl7Aqqq67333uPVV1+1Oka5u3DhArGxsSxYsAA/Pz+WLFmSt+7EiRNMmjQp73nb\n+vWp5uFBxLRp/HDkCP3uuw+Axdu28bitByvAlCeeYHlkJMsiI2kdGMirDz/Mv3/+mfsmTaLjlCnU\n9fXlgeBg+zVSVUovvvgiH374odUxlKoQZRma5C1Kf+asNDYDzUSkCXAMeAp4upT7Lgcm5+v08Cgw\nphyzKWWZgwcP4uXlRWBgoNVRyt3+/fsxxhAWFsbmzZsLrKtbty5jx44t8NrUfv1uOMaQhx4q9vgb\noqMB6N6mDd1tvV5L4+eTJ3n6o4/Yd/Ik0/r3Z8vhwzzcogVPhoUVu09Wdjb3TJzIytdeI8DHp9jt\nWsbE8OdnniGiRYtS51Hlr3Xr1syfP59z585Rq1Ytq+MoVa7KMmjweGPMhJKWMhwvExhKTmGWCHxu\njNklIm+JSG8AEblfRI4C/YG/iMgu277ngLfJKQg3A2/ZXlOqyps1axa///3vrY5RIVJTU4GcCdEr\nk3FLlvB0+/ZcnD6drq1bs3rPHvrde+9N93F1ceGlTp2Yahv3zioR06bhNWQINYYNo8awYXSbMSNv\n3anUVLpOn4730KFExMWxa8+eAvu+/PLL+Pn50bdv3wKXIHv06MH3339vtzbYy7Bhw5iR7+ejlKMo\nVTEnIv4iEi4iTcvzzY0x3xhjmhtjmhpjJtleizHGfGl7vNkYU98YU90YU9sY0zrfvh8bY+6yLXPK\nM5dSVtmwYQNhYWFUq1bN6igVIi0tDah8xdyaffvoa7s/ce7GjTweGoqLS8l/Hvvfdx+ffP89mVlZ\nFR3xpv76/POkz5hB+owZLM03U8grn31GsL8/Z+Pj+X1EBOMmT86b4mrTpk3s3buXkydP4uXllTeX\n6dKlS6lTpw7h4eGWtKUi+fv74+fnx969e62OolS5uulfKxFxEZE/AynAd8A+EdkgInoDmlLl7MqV\nKyxYsIABAwZYHaXCpKen4+rqipdtfDirXbxyheqvvsqZ9HRaT5jAb+fMYfnu3XS+664C27386acM\n/fvfAcjMyuLh+HgmffMNdX19qVmtGtuS/9e5ftOBA7QePx7fyEhGLVxYquNUhLSrV/nXTz/xZs+e\nVPPw4Mn778fb25u1a9cCcPjwYTp27IiHhwcPPvgghw4dIiMjg5iYGGJjY29+8CrslVdeYebMmQXG\nLVSqqivpq+dQYDA5Y8wtAn4COgJ/qeBcSjmduLg4/vCHPzjkUCS50tLSKtVZOd9q1Vg2bBhhjRqR\nPmMGfxs4kF3Hj9MsIKDAdq9368YnmzZxMjWVofPnU8/Xl7HduwPQom7dvF631zIyeOIvf2HkI49w\neto0vNzdScrXk/5mx8nVc+ZMar72WpFL7LJlRbbj1fnz8R8xgkcSEvKy/HzqFDW9vQvczxfcqBG7\nd+8GoGXLlmzYsIGrV6+ybt06QkJCmDlzJn379nXI+zVzeXp6MmjQIN5//32royhVbkrqAPEcOfez\nPWCMSQMQkQ+A50WkpjHmQkUHVMoZrF+/nkaNGtGwYVlG96l60tPTK1UxB7Dj6FHaBP1vmMqLV65Q\no9CMG41q1+bJsDAemz4dbw8P1uSbYuwOT08uXrkCwMYDB/D28GDgL34B5BRvU1euLNVxcv1r6NAy\n5f9j376EBAbi6uLCe2vW0P2999gzYQKXrl3Dp9AZ0Ore3qSnpwPQrl07unXrRnh4OA899BDh4eGM\nHz+elStX8vzzz3Po0CEGDRrEb37zmzLlqQpCQ0NZtWoViYmJtGrVyuo4St22ks7MtQD+mlvI2bxH\nzlyqzSsslVJOJC0tjUWLFvHcc89ZHaXCpaWlUaNGDatjFLDj2DHa1KuX99y3WjXSbfeV5dc2KIjt\nR48y+9ln8XR3z3s97do1anp7A3AiNZUGfv+bWdDT3Z07CxWvxR3nVrVv0oQaXl5U8/Ag+rHHqOHp\nyX8PHaK6p2eB8fYALl2+XODnP2bMGLZv305CQgIxMTGMGzeOTz/9lObNm7NixQoSEhI4e/bsbWes\njCIjI5k1a5aOPaccQknFXHVuHL/teL51SqnbNGXKFEaPHu3Ql1dzVcYzcz8dO1bgzNzdQUHsO3my\nwDbf7d/P1JUr6dOuHXM3bSqwbs+JE3n71/Xx4ej583nrrmdmciotrVTHydVtxoy8nqmFl8mluL8u\nt+NGszvv5Pzly5y09SAGOHj4MCEhhafAhh07dnDgwAF+9atfkZiYSFhYGB4eHjRv3pykpKQS37Mq\ncnNzY+jQoUyfPt3qKErdttKMM1d4bLnc547/yaNUBVu2bBmhoaHUrVvX6ih2UdnOzBlj2Hn8eIFi\n7tFWrdiQlETvdu0AOHTmDE998AHzX3qJAB8f7ps0iejHHqNOjRqcuHiRi1eucE+DnDHMOwQHk37t\nGn/buJGn27fnnaVLuZaZWeJx8svfG7UkFy5fZvOhQ3Rp1gwRYdbatZy/dIn7GzfmDi8verZpw9tf\nf83Ufv34x5YtpF++TERExA3HGTlyJNOmTQOgUaNGrFmzho4dO7J161aHvvTfsmVLVq9ezdatW7m3\nhKFolKrMSjM0SXcRicpdgN+RU9D1z/+6bRlesXGVchznz59n1apV9CtiYFxHVdk6QBw6exYvd3fu\nzNdJ4LkOHVj8449kZ2eTdvUqvd9/n4l9+tCxaVOa+vvTo02bvLHl/vHDD/wmPBw3V1cg57LqFy+/\nzJTly6kTFcXl69e5y9+/xOPcqoysLMYsXkztESOo+4c/8K8dO1g6bBh32O6V+9Mzz/DzqVPUGj6c\nmatXM+n11/EsdD/gokWLaNasGW1sgywPHjyY7777joYNG/Lcc885dGcIyOndOmfOnLwhW5SqisSY\n4id1EJGy9t02xhjX24tUMcLCwsyWLVusjqFUnujoaEaPHu1Uo9H36tWLmjVr8sknn9x0u2/nzeP+\nM2fwLWIIk7kbN/K3jRvJMoa5Awfy07FjxNmKor0nTvDnZ56hj226r/iVK1m0bRsboqM5dOYM4bGx\ntAoMxMPVlRWvvVbs+//us8+IaN6cAfffX+w2uTNArIiMpK6vb2mab6kT6ekktWhBpx49rI5S6Rw8\neJB58+bdMAOJUlYSkR+MMcVPQ5NPSZdZi583Ryl1yxYuXEhERIRTFHKZmZkEBQUxd+5cEhMTb6t3\n5LHz5/l3UhKr8vUCbVirFj1sZ5XC33mHX7ZsCeQME7LdNkxHrkdateLTQYNKfJ8/PfNMidu4uriw\nIyamLPFVJdWkSRMCAwP5z3/+wy9sPZGVqkpuepnVGLOurIu9gitVVZ08eZIffviB7oXGF3NUbm5u\nvPTSS3Tt2hUXFxdeeeWVWz7W8t27ycrO5pfx8UQuWFBg4Nf9p08T6OtLDdvZvA83bOC3HToU2H/N\nvn10jotjxurVt5xBOaaBAwfy+eefc+nSJaujKFVmpZ6bVSl1+4wxxMbGMmbMGKuj2NXEiRM5fvw4\nu3fvJqDQgLxlcTI1lasZGayKisLLzY0l27fnrVu4dSu/sk3JlZGVxbqff+Zh21k6gEBfX/a99RZr\noqJYsXs3Px07dusNUg5HRBg1apRDz36hHJcWc0rZ0aeffkqfPn0qVScAewkMDMTN7cY7O44dO0ZE\nRESB5a1ihovwrVaNB5vnDHH5cMuW7E5JyVv31Y4d9G7bFoBPNm3i6fbtC+zr6e5OdU9P3Fxd6dGm\njRZz6gb16tWjdevWrMw30LNSVYEWc0rZSXJyMgcOHChyaAhnFhQUxNq1awssMZGRRW7bsWnTvOmq\nfkxOJrhOHQCOX7iAt4cHftVzhr/ce+IEf1q3jq7Tp7MrJYX3Vq8uMIDuf5KS8vZVKr8BAwawfPly\nLlzQCY5U1aHFnFJ2YIwhLi6O6Ohoq6NUGSdTU2+YhD60QQOqeXgQMW0aPxw5Qr/77gNg8bZtPG7r\nwQow5YknWB4ZybLISFoHBvLqww/z759/5r5Jk+g4ZQp1fX15IDjYru1RVYOIMHr0aL3cqqqUmw5N\n4kh0aBJlpdmzZxMaGkr7Qpf+VNFuNjSJujU6NEnZfPXVV2RnZ9OnTx+roygnVZahSfTMnFIVbPPm\nzaSnp2shp1QV0qtXL7Zs2eKw05kpx6LFnFIV6MiRIyxYsIDhw3VyFKWqmpiYGBISEjifb75dpSoj\nLeaUqiBpaWnExsYyceJERHQqY6WqGnd3d95++23GjRtHRkaG1XGUKpYWc0pVgKysLMaNG8eECRPw\n0vu+lKqy/Pz8iIqK4s0338RZ7jFXVY8Wc0pVgIkTJ/Lyyy/j7+9vdRSl1G1q2rQp3bt3Z+bMmVZH\nUapIWswpVc4+/PBDOnbsSEhIiNVRlFLlpFOnTtSuXZslS5ZYHUWpG2gxp1Q5WrFiBQCPPPKIxUmU\nUuXt6aefJjExka1bt1odRakCtJhTqpzs2rWLjRs38uKLL1odRSlVQaKjo/nss884ptPBqUrE0mJO\nRLqKyF4RSRKR0UWs9xSRBbb134tIY9vrjUXkioj8aFv+bO/sSuV36tQpZs+ezbhx46yOopSqQC4u\nLkycOJHJkyeTnp5udRylAAuLORFxBWYB3YAQ4NciUvgmo0HAeWPMXcC7wJR86/YbY0Jtyyt2Ca1U\nEa5evcqECROYNGkSrq6uVsdRSlWwatWqERMTw7hx48jKyrI6jlKWnplrDyQZYw4YY64D84HC86b0\nAf5me/wF8EvRAbtUJWKM4Y033mD06NHUqFHD6jhKKTsJCAjgxRdf5J133rE6ilKWFnNBQHK+50dt\nrxW5jTEmE7gI1LatayIi20RknYh0ruiwShVl6tSpDBgwgAYNGlgdRSllZ3fffTdhYWHMmTPH6ijK\nyVlZzBV1hq3wiIzFbZMCNDTG3ANEAfNExOeGNxAZLCJbRGTL6dOnbzuwUvl98MEHNGvWjLCwUs2D\nrJRyQF27dsUYw8KFC62OopyYlcXcUSD/6Yz6wPHithERN8AXOGeMuWaMOQtgjPkB2A80L/wGxpjZ\nxpgwY0yYDt6qyosxhj/+8Y/Ur1+fxx9/3Oo4SimLvfDCC1y5coWPPvrI6ijKSVlZzG0GmolIExHx\nAJ4Cviy0zZfAb22P+wGrjTFGRPxtHSgQkWCgGXDATrmVE8vKyiImJobOnTvTrVs3q+MopSqJZ599\nloCAAKZNm6bTfim7s6yYs90DNxRYDiQCnxtjdonIWyLS27bZR0BtEUki53Jq7vAlXYAdIrKdnI4R\nrxhjztm3BcrZXLt2jejoaJ566ik6dOhgdRylVCXTs2dPwsPDGT9+PNnZ2VbHUU7Ezco3N8Z8A3xT\n6LWYfI+vAv2L2G8hoDcoKLtJT09nzJgxjBw5kkaNGlkdRylVSXXq1AkfHx+io6OZPHkyHh4eVkdS\nTkBngFCqBGfOnGHUqFHExMRoIaeUKlHbtm0ZMmQII0eO5NKlS1bHUU5AizmlbuLIkSOMHz+e2NhY\ntBONUqq0mjRpwtixY4mOjubs2bNWx1EOTos5pYqxe/duEhISmDZtGnfccYfVcZRSVUxAQADvvPMO\nb775JsnJySXvoNQt0mJOqSJs2rSJefPmERcXh6enp9VxlFJVlI+PD1OnTiU+Pp49e/ZYHUc5KC3m\nlCrk66+/Zt26dbz99ts616pS6rZ5eXkxdepU5s6dy3fffWd1HOWAtJhTyuby5cvExMSQnp7OqFGj\n0GmAlVLlxdXVlUmTJrFz506mTJlCRkaG1ZGUA7F0aBKlKovvv/+eefPmER0dTVBQ4SmClVLq9okI\ngwcPZt++fQwfPpwhQ4bQqlUrq2MpB6Bn5pRTu379OrGxsWzfvp2EhAQt5JRSFa558+YkJCTwzTff\nMGvWLB1gWN02LeaU09q1axdRUVE88cQTDB48WC+rKqXsxs3NjREjRtChQwciIyM5fPiw1ZFUFaaX\nWZXTyc7O5v333ycjI4OEhATc3PTXQClljXvvvZeQkBDi4uJo3Lgxzz77rH6xVGWmZ+aUUzl06BCR\nkZF06tSJ4cOHayGnlLKcl5cXb7zxBg0bNiQqKopTp05ZHUlVMfpJppxCdnY2c+fOJTk5mbi4OLy8\nvKyOpJRSBTz44IPcc889xMbGcv/99/P444/rWTpVKnpmTjm07OxsFi1axMiRI2nRogVvvPGGFnJK\nqUrLx8eHyZMn4+3tTVRUFCtXrsQYY3UsVclpMaccUnZ2NosXL2bkyJHUrl2b+Ph4OnToYHUspZQq\nlccee4z4+HiuX79OVFQU3377rRZ1qlhazCmHYoxh8eLFjBgxglq1ahEfH8+DDz5odSyllCozEaFH\njx7Ex8dz9epVoqKiWLVqlRZ16gZazCmHYIzhn//8J1FRUfj5+fHuu+9qEaeUcggiQs+ePYmPj+fy\n5ctERUWxevVqLepUHi3mVJVmjGHJkiVERUVRs2ZN3n33XSIiIqyOpZRS5U5E6NWrF/Hx8aSnpxMV\nFcWaNWu0qFPam1VVTXv37mXhwoWkpqby6KOPEh8fr72+lFJOQUTo3bs3vXr14quvvmLMmDHUqVOH\n/v3706hRI6vjKQtoMaeqjOPHj/OPf/yDlJQUWrRowZAhQ/D19bU6llJKWSK3qOvduzenT5/miy++\n4MiRIzRu3Jh+/fpRu3ZtqyMqO9FiTlVqFy9eZOHChezbt4969erx5JNPEhgYaHUspZSqVPz9/fnd\n734HwMGDB5kzZw5nzpwhNDSU3r174+3tbXFCVZG0mFOVzqlTp1i7di3btm3Dx8eHvn378sILL1gd\nSymlqoQmTZowcuRIjDFs376dqVOncvXqVR544AE6d+6Mn5+f1RFVOdNiTlnu6NGjrF+/nsTERIwx\n3HnnnXTp0oX+/fvrfXBKKXWLRITQ0FBCQ0PJzs5m8+bNfPzxx1y4cAERoW3btnTu3JmAgACro6rb\npMWcsitjDPv372f9+vUcOHAAEaF+/fp06dKFX//611q8KaVUBXBxcSE8PJzw8HAAsrKy2LlzJ59/\n/jknT55ERGjZsiVdunShQYMGFqdVZaXFnKow586dIzExkcTERJKTkzHGYIyhadOmREREMHDgQC3e\nlFLKAq6urrRr14527doBOV+09+7dy9KlS0lOTsbFxQURoXHjxoSEhNCyZUt8fHwsTq2KY2kxJyJd\ngemAK/ChMSa20HpPYC5wH3AWGGCMOWRbNwYYBGQBw4wxy+0YXdlcv36dlJQUkpKSSExMzPuGJyLU\nrFmTkJAQHn30UerXr4+Liw5rqJRSlVHumbmWLVvmvZaVlcXhw4dJTExk/fr1pKam5q2rV68erVq1\nIjg4mLp16+Lu7m5FbGVjWTEnIq7ALOAR4CiwWUS+NMbszrfZIOC8MeYuEXkKmAIMEJEQ4CmgNVAP\n+FZEmhtjsuzbCseVkZHBuXPnSElJ4dixYxw/fpwTJ06QmZlZYDsPDw8CAwMJDg7mySefxN/fX8+2\nKaWUA3B1dSU4OJjg4GB69OiR97oxhpSUFHbv3s2yZcuK/Gxwd3enXr161KtXj6CgIOrWrYufnx9u\nbnpBsCJY+VNtDyQZYw4AiMh8oA+Qv5jrA4y3Pf4CmCk5lUIfYL4x5hpwUESSbMfbaKfslY4xhuvX\nr3P58uW85dKlSwWe5y5paWlcvHiR7OzsYkcOd3d3x8/Pj8DAQIKCgmjXrh0BAQH67UsppZyciOQV\nasW5du0aJ06c4NixY+zdu5e1a9dy4cKFG4q+3OMZY3Bzc6NmzZrUqFEDb2/vG5bq1asXeO7u7q4n\nD2ysLOaCgOR8z48C4cVtY4zJFJGLQG3b65sK7RtUcVFLZ9OmTSxbtqxU2xpjSvWfMH+xVdL2np6e\nxf4C1KpVq8BzX19f/YakKi0XDw+2X7mC27VrVkdxGNczM/HQ33llJ56enjRq1KhMM1JkZmZy4cKF\nG05EXLx4kZSUlBtOTFzL9/fhZp+PxX3e5n6+5q4r7ecyQL9+/bj77rtL3baKZuVvdlE/scKniYrb\npjT7IiKDgcG2p+kisrdMCW9NHeCMHd6nMnLmtoNzt1/b7rycuf3O3HZw4vZPmDDBHm0vdSVsZTF3\nFMjf/7k+cLyYbY6KiBvgC5wr5b4YY2YDs8sxc4lEZIsxJsye71lZOHPbwbnbr213zraDc7ffmdsO\nzt3+ytZ2K7sXbgaaiUgTEfEgp0PDl4W2+RL4re1xP2C1yTkv+iXwlIh4ikgToBnwXzvlVkoppZSq\nNCw7M2e7B24osJycoUk+NsbsEpG3gC3GmC+Bj4BPbB0czpFT8GHb7nNyOktkAkO0J6tSSimlnJGl\nd8MaY74Bvin0Wky+x1eB/sXsOwmYVKEBb41dL+tWMs7cdnDu9mvbnZczt9+Z2w7O3f5K1XYpbmgK\npZRSSilV+emQ/EoppZRSVZgWcxVIREaKiBGROlZnsRcReVtEdojIjyKyQkSKH1XSwYhInIjssbV/\nsYjUtDqTPYlIfxHZJSLZIlJpenlVJBHpKiJ7RSRJREZbnceeRORjETklIjutzmJvItJARNaISKLt\n/3yk1ZnsRUS8ROS/IrLd1vYJVmeyNxFxFZFtIvIvq7Pk0mKugohIA3KmKjtidRY7izPGtDXGhAL/\nAmJK2sGBrATuNsa0BfYBYyzOY287gb7AequD2EO+KQm7ASHAr21TDTqLvwJdrQ5hkUxghDGmFfAA\nMMSJ/u2vAQ8bY9oBoUBXEXnA4kz2FgkkWh0iPy3mKs67QDRFDGbsyIwxqfmeVseJ2m+MWWGMyZ2r\nZhM54x86DWNMojHGHgNzVxZ5UxIaY64DuVMSOgVjzHpyRhlwOsaYFGPMVtvjNHI+2C2fhcgeTI50\n21N32+I0f+dFpD7QA/jQ6iz5aTFXAUSkN3DMGLPd6ixWEJFJIpIMPINznZnL7wVgqdUhVIUqakpC\np/hAV/8jIo2Be4DvrU1iP7bLjD8Cp4CVxhinaTuQQM6Jmmyrg+SnE/XdIhH5FqhbxKqxwOvAo/ZN\nZD83a7sxZokxZiwwVkTGAEOBN+0asAKV1HbbNmPJuQzzmT2z2UNp2u9ESjWtoHJcIlIDWAi8Vuiq\nhEOzjesaarsveLGI3G2Mcfh7J0WkJ3DKGPODiERYnSc/LeZukTHm/4p6XUTaAE2A7bYJe+sDW0Wk\nvTHmhB0jVpji2l6EecDXOFAxV1LbReS3QE/gl8YBx/0pw7+9MyjVtILKMYmIOzmF3GfGmEVW57GC\nMeaCiKwl595JIjh0nQAAAUJJREFUhy/mgF8AvUWkO+AF+IjIp8aYZy3OpZdZy5sx5idjzJ3GmMbG\nmMbk/MG/11EKuZKISLN8T3sDe6zKYm8i0hUYBfQ2xly2Oo+qcKWZklA5IMn5pv4RkGiMibc6jz2J\niH9uT30RqQb8H07yd94YM8YYU9/22f4UOVOMWl7IgRZzqvzFishOEdlBzqVmp+myD8wE7gBW2oZm\n+bPVgexJRH4lIkeBDsDXIrLc6kwVydbZJXdKwkTgc2PMLmtT2Y+I/B3YCLQQkaMiMsjqTHb0C+A3\nwMO23/UfbWdrnEEgsMb2N34zOffMVZohOpyVzgChlFJKKVWF6Zk5pZRSSqkqTIs5pZRSSqkqTIs5\npZRSSqkqTIs5pZRSSqkqTIs5pZRSSqkqTIs5pZRSSqkqTIs5pZRSSqkqTIs5pZRSSqkq7P8BaAXQ\nSRbMaIkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1065f9f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -.6745, .6745 # integral limits\n",
    "\n",
    "x = np.linspace(-4, 4)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-.6745}^{.6745}f(x)\\mathrm{d}x=$\" + \"{0:.0f}%\".format(result_50p*100),\n",
    "         horizontalalignment='center', fontsize=11.5);\n",
    "\n",
    "ax.set_title(r'50% of Values are within .6745 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/interquartileRange.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "50% of the data is within .6745 standard deviation (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showing IQR with Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAKACAYAAAAMzckjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x150a505450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(39)\n",
    "\n",
    "# 8, 11, 20\n",
    "\n",
    "# connection path is here: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs\n",
    "mu, sigma = 0, 1 # mean and standard deviation\n",
    "s = np.random.normal(mu, sigma, 1000)\n",
    "\n",
    "fig, axes = plt.subplots(nrows = 2, ncols = 1, figsize=(9, 9))\n",
    "\n",
    "# rectangular box plot\n",
    "bplot = axes[0].boxplot(s,\n",
    "                vert=False,\n",
    "                patch_artist=True, \n",
    "                showfliers=False, # This would show outliers (the remaining .7% of the data)\n",
    "                positions = [0],\n",
    "                boxprops = dict(linestyle='--', linewidth=2, color='Black', facecolor = 'Red', alpha = .4),\n",
    "                medianprops = dict(linestyle='-', linewidth=2, color='Yellow'),\n",
    "                whiskerprops = dict(linestyle='-', linewidth=2, color='White', alpha = .4),\n",
    "                capprops = dict(linestyle='-', linewidth=2, color='White'),\n",
    "                flierprops = dict(marker='o', markerfacecolor='green', markersize=10,\n",
    "                  linestyle='none', alpha = .4),\n",
    "                widths = .3,\n",
    "                zorder = 1)   \n",
    "\n",
    "axes[0].set_title(r'50% of Values are within .6745 STD', fontsize = 24);\n",
    "\n",
    "axes[0].set_xlim(-4, 4)\n",
    "axes[0].set_yticks([])\n",
    "x = np.linspace(-4, 4, num = 100)\n",
    "constant = 1.0 / np.sqrt(2*np.pi)\n",
    "pdf_normal_distribution = constant * np.exp((-x**2) / 2.0)\n",
    "\n",
    "axes[0].annotate(r'',\n",
    "            xy=(-.6745, .30), xycoords='data',\n",
    "            xytext=(.6745, .30), textcoords='data',\n",
    "            arrowprops=dict(arrowstyle=\"|-|\",\n",
    "                            connectionstyle=\"arc3\")\n",
    "            );\n",
    "\n",
    "axes[0].text(0, .36, r\"IQR\",  horizontalalignment='center', fontsize=18)\n",
    "axes[0].text(0, -.24, r\"Median\", horizontalalignment='center', fontsize=18);\n",
    "axes[0].text(-.6745, .18, r\"Q1\", horizontalalignment='center', fontsize=18);\n",
    "#axes[0].text(-2.698, .12, r\"Q1 - 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "axes[0].text(.6745, .18, r\"Q3\", horizontalalignment='center', fontsize=18);\n",
    "#axes[0].text(2.698, .12, r\"Q3 + 1.5*IQR\", horizontalalignment='center', fontsize=16);\n",
    "\n",
    "axes[1].plot(x, pdf_normal_distribution, zorder= 2)\n",
    "axes[1].set_xlim(-4, 4)\n",
    "axes[1].set_ylim(0)\n",
    "axes[1].set_ylabel('Probability Density', size = 20)\n",
    "\n",
    "##############################\n",
    "# lower box\n",
    "con = ConnectionPatch(xyA=(-.6745, 0), xyB=(-.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# upper box\n",
    "con = ConnectionPatch(xyA=(.6745, 0), xyB=(.6745, 0),\n",
    "    coordsA=\"data\", coordsB=\"data\", axesA=axes[1], axesB=axes[0],\n",
    "    arrowstyle=\"-\", linewidth=2, color=\"red\", zorder = 2, alpha = .2)\n",
    "axes[1].add_artist(con)\n",
    "\n",
    "# Make the shaded center region to represent integral\n",
    "a, b = -.6745, .6745\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(-.6745, 0)] + list(zip(ix, iy)) + [(.6745, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "axes[1].add_patch(poly)\n",
    "\n",
    "##############################\n",
    "xTickLabels = [r'$-4\\sigma$',\n",
    "               r'$-3\\sigma$',\n",
    "               r'$-2\\sigma$',\n",
    "               r'$-1\\sigma$',\n",
    "               r'$0\\sigma$',\n",
    "               r'$1\\sigma$',\n",
    "               r'$2\\sigma$',\n",
    "               r'$3\\sigma$',\n",
    "               r'$4\\sigma$']\n",
    "\n",
    "yTickLabels = ['0.00',\n",
    "               '0.05',\n",
    "               '0.10',\n",
    "               '0.15',\n",
    "               '0.20',\n",
    "               '0.25',\n",
    "               '0.30',\n",
    "               '0.35',\n",
    "               '0.40']\n",
    "\n",
    "# Make both x axis into standard deviations\n",
    "axes[0].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "axes[1].set_xticklabels(xTickLabels, fontsize = 14)\n",
    "\n",
    "# Only the PDF needs y ticks\n",
    "axes[1].set_yticklabels(yTickLabels, fontsize = 14)\n",
    "\n",
    "##############################\n",
    "# Add -2.698, -.6745, .6745, 2.698 text without background\n",
    "axes[1].text(-.6745,.41, r'{0:.4f}'.format(-.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(.6745, .410, r'{0:.4f}'.format(.6745) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(-2.698, .410, r'{0:.3f}'.format(-2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "axes[1].text(2.698, .410, r'{0:.3f}'.format(2.698) + '$\\sigma$', horizontalalignment='center', fontsize=14,\n",
    "            bbox={'facecolor':'white', 'edgecolor':'none', 'pad':5});\n",
    "\n",
    "\n",
    "axes[1].text(0, .04, r'{0:.0f}%'.format(result_50p*100),\n",
    "         horizontalalignment='center', fontsize=18)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('images/IQRboxplotDistribution.png', dpi = 900)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within 2 Standard Deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-2}^{2}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9544997361036417\n"
     ]
    }
   ],
   "source": [
    "# Make the PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -2 to 2\n",
    "result_n2_2, _ = quad(normalProbabilityDensity, -2, 2, limit = 1000)\n",
    "print(result_n2_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAAFICAYAAAA75Xj9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3XmclXP/x/HXZ6Z936WNUJEomQpplZ1wC9m5b9vvlvVGItFmj+xkue2yhLJLkrtslaJCSmgTZYk0NU3z+f1xXUfHNHPmnGlmrlnez8fjPGau/XPOnLnO53xXc3dEREREpGxKizoAERERESk8JXMiIiIiZZiSOREREZEyTMmciIiISBmmZE5ERESkDFMyJyIiIlKGKZkTKSXMrKmZPWRmy8xsk5m5mb0XdVwFMbPpYaynRB2LFC8zGxX+rR8q6ePNrF947OLCXFukPFMyJ8XGAieb2RQz+9nMNpjZt2Z2v5m1TnDcjuFNu6BHRj7H72Fmr5nZ72b2p5lNNbPuBcT6jJltzu+cxc3MKgHvAv8CWgB/AD8CvxRw3LTwtXg9hWvdEh6zwsx0D5AiYWaXmtl1ZtYq6liKkpntZmZXm9nbZvaDmWWZ2Voz+9jMrjKzutt4/oZmNtTMPjSzX8LzrzKzuWb2tJmdY2Y7xu2/PMn7Y+7H4rhzTM9j+0YzW21mX5nZs2Z2iZltty3PTUpOpagDkPLJzCoDzwNHhauyCRKUHYFzgZPN7Ch3f7eAU/2YYNumPK7bFpgB1A6vuRnoDbxrZge4+/Q8jukLDATuc/dZBcRTXA4GdiNI3vZx90VJHvco0BM4yMyauvuqRDubWTpwUrj4pLvnFDJeqZhWAwuBH/LYdinQHHgHWFoM1/4zvPb3xXDuPJlZL+C9uFUOrAXqAl3Dx3lmdoi7f1GI8+8LTAQax63+HagFdAwfJwITgAHh9p/I+7O7LlANyAJ+zWP76jzWZYbXg6Bwpw7QCGgHHA/cZGYPApe7+/qkn5iUOH0rl+JyE0Eilw1cAtR19wZAS4Ikrxbwopltn+gk7t40weOzPA65jiCRe5TgxlQbuBmoAtyYe2czqwLcS3Cju7pQz7Ro7B7+nJpCIgfwArAeiE/SEukHNAt/fyyF64jg7ne4+67ufk0E1/4wvPbBJXjZygRfGp8GDgNqu3t9gvvXqcDPBPe0V8ysWionNrMGwCSCRO5rgqSttrvXdfdaBP+nJwIvE9xHAXD3znndDwkSPoD/5XO/3DePMJ6O297E3asBTYFjgbfD5/9vYIaZ1Url+UnJUjInRc7MmgDnh4u3ufvY2Lc6d19OcIP6kuCb5NAivvwBBKVxF7l7prtvIkjSfgT2NbMaufa/nOBb6OXunte32ZJSPfy5LpWD3P0P4MVw8dQkDjkt/DmrMCUJIhXMQqCdu5/s7m+4+58A7r7e3Z8ETgj324kgAUrFSQSlYJlAb3cf7+5//f+7+w/humOAM7f5mSTJ3X909xfDpPlsgtLITsADJRWDpE7JnBSHvgQlYQC3597o7puBO8PFE8Mq2aLSEFjj7rGqA9w9m6BqJg2oH1sftkO5GpgOPF5UAZhZHzN7MWz3Emv/8lJYnZt730fNzAlKFAFOz9WOZcckLhkrYetkZnskiKs2cHSuY2LbqprZkWb2sJl9FtfG8Xsze8LM9koijtzXOyt8Du8k2KfABvFm1t/MJsW9nj+GywcmOGavMO7vwrZAf5jZEjN7w8wuMrPq+R2bz/n2NLNrw7ZGS8Nz/mxBe8x/5tf2MP75mVmamV1oZjPDNlduZh1y7d/EzG40s3lmts6CNp/zwvPUz+saCWLuE15jZR7bKoWviZvZ53lsr2Nm2eH2Fnk9n9zrCKpYAf6X6z2c6O9/ppl9Ej7XtRa0rz0gn33z7QBhcZ1wzKyGmY0ws6/D9/CPFrQ92znxK7Y1d1/m7t8m2D4FWB4u7p3i6WP/q5+6e17V1vHXyUzx3EXC3R8C7ggXTzSz9lHEIQVTMifFYYfw59oEbbi+Cn/WBzoX4bV/BhqZWZ3YCgvaie0A5PD3tiR3ElYjuLsXxcXNbBRBR4ZjgCYE7XyaECRRU8zshlyHrCUoNfwzXN4QLscem5O47Lts+UA5LcF+A4AaBNVGz+TadihBlc8/gT0J2t440Ao4BfjEzJKpxi0yZlbFzJ4haFN0JLAdQSlGk3D5bTO7Po/jjgQ+IYg79nd3oDVwCDCWLYlHst4nSLi7E1R/ZQINCNpjPgy8FL7P8pNG8PreQVDKsVVbRTPrSVASNBjoQPDetPD3q4E5ZtYmhZg/Img/tX0ex3UmqCoE6GBmDXNt35+g6n5JWJqeSKyzTuw5/cLf38N5duIxs/8CjwB7hcfWIfgi+LaZHZXXMUmoC3wIXENQ/ZlD8H45EfjIEnS82gY/hz8T/f0TaVbwLpG6ieCeYQSvo5RCSuakOMQSo0Tvr/gGvLvnt5MFPbx+N7NMC3rCPmlm+yc477sEN9U7zKyaBb1ERxIkAh/FqnvNrD9BQnCnu89L4jkVyMwGsqXd3d1Ak7B9TWPgrnD9lRY3hIe7XxS2d7k1XPVsrnYuywq6btiJ4Ylw8aT8SonYkui96u4/59r2B0FS0hdo6O413b06QYeVuwj+Xg+aWapJ0LYYQ9AxZUn4s7a71yVoB/l/YcxDzOy42AFmZgSvfSWCJLCtu1d39zoEH/S9CZ7nxhRjeY+gp3EroKq71yNIhk4naJDeH7gwwfHHETQBOI+g/Wh9grZJ34dx7wS8AtQjqM5qS1D1XpOgBOdtgsR0QgFJ41/C0pyZ4WKvXJtjy38QfEj3yGf7tCSuc1P4Ho6VLh2V6z18fB6HHUtQRXkuwetRB9iZoJQ8Dbg72eeZyyiCv8tBBK9dLYK/+UqCKs3RhThnvsysMRArrZqf4uGxzlatzWykBe13S53wC/nccDH3+0RKC3fXQ48ifRDcpD18tMxnnwvj9hmaa9uOcdsc+I2gJCR+3VjA8jjvbgQfUE7wbXJD+HsW0DPcpwbwHbCCIEEoiudswKLwWs/ks8/T4fbvgLRc264Ltz1ayOu3i3ttDspjeyu2lFAdVYjzPxYee3Ue26aH207Jtf6scP07Cc47KtznoVzrdw3j/RnYIZ9jTwqPnRu3rlnc69CohN7vfcLrLUrw/Bz4Z4JzjA/3GZPP9qrAvHCfo1OIbXR4zBO51r8aro9tvz3X9o/C9acn8/cKty0Pt+2fxN/bgRPy2N4i/F91YL9c2/qF6xcneA/+CeyUx/bYPWk9UKkI//Z3saWHa8MUj60Rd89wghLMF4ArCBLQGime78mC/t/yeL22+jvms//D4f7fF9Vrp0fRPlQyJ8VhKsENGYIqo78Jv4FeHLeqdq5dNhD0MO1JkGzVI7jx7U1QegFwETAk97nd/UuCb49vEpS+5BBUkfVz9/fD3a4hKOW41N3/CNspPRa2gVpvZu+aWartXzoBu4S/j8pnn+Hhzx0IhjQoMu6+EPg4XMyrqvVUgoRzDZD0mHRxYq97wvH6itDpBPG+6O75DUXxAkHC3jEsIYFgmIVYyXDT4g3xL+8RfIHYxYLOP3lZTT69hy3oJRhrPL9VG1MAd9/Ilt6K+bYVzEPsPf9XyVxYcrs/QQJyVx7ba7Gl/VeBJXOFtMTdn8290oMq3dnhYofc25PwrLsvyWP9xPBndYLOCtvMzA5jS0evob51aXdCHtQS9AbeCFfVJ3gf3ERwD/3NzCaaWbeiiHcbxZqnNIg0CsmXkjkpcu7+E3B/uPhvMxttZi3MrLIFDelfJ2i/FBsnLifX8avc/Xx3/5+Hvbs88Km79ycY2gTgKjOrl8f157r7oe5ey91ruHuvWCJnZrsSjIf1jrs/a8FwAu8SJEBzCNo1dQfeM7PdUnjasXZ/q919QT6vy0KC0sD4/YtSLFk4xrYeRiDW0/UZD3r4bsWCwUuvtS2Dl8YawDtbXvOSat+zX/jzBAs6Pmz1IBjLLFYV1xIgfL/ExhKcbMFgrx0TVD0nxQLHhx+uy8KG9bHXJoctX0jye30+8aDjT166EFQLOzArwfO9JP65JmkGwbAWLePai3UiqHL+nwdVaF8SJMSx/6X9wniWuvt3KVwrFYnGc4z9j6TU4SM0M6+V7r6BLW3bCnPev7Gg48pTBF84Jrr7XQUckid3X+HuhxE0NbkaeA2ItTOuTFB9/4GZDdrWmItIkbQtlqKnZE6KyxUEpTkGXAUsIyit+5Sg7dA9BG2hIKhGTUWstK9meK5U3BP+jN0czya4kd7n7v3cfSBB26ha5F/ClpdYydCKhHtt6ajQOOFehTOeoDSyBnHDJITf7NuFi/mVDu0BfEFQ3bsPwQfeeoL2YD+y5Zt5zWKIOy+x8QdrE7R3zO8Ru4fFDznzT4KOBE0J/oZzCUo5XjGzk1Jti2VBb+uXgWcJPlxjvTvXsKWRf+wLSX6vT14DtsbEnquR+LnGOvXkHl4nX2FyOydc7JXr53vhz2kEr+P+ubYXV6kcBCWZ+dkQ/ixML/fiOu9fwl6xbxO0b5xOcuM7JuTuX7j79e5+hLtvT9AObwRB85I0gjbAe27rdbZBLAGOcvgmSUDJnBSLsFroKIJRxCcCi4FvCaoU/kFQzRqb9ieVQXLxYKiA2Idj0lUmZnYyQQP/W8NSMoAjwp93x+36dHj+gwvRCLtqivsXGQ/GyZsULsZXtcZ+X+Dus8nbfwl6/c0iaDxey93ruPt2HjRuj/VisyIOOz+xe9P57m5JPP6a2cPdFxNU0f0DeJCg53Rtgr/1U8CHZpZKUnoeQRL3J3ABQTvQau7e2LcM2PpTuG9+r0+iXsmx57o6yefaL4XYYUtSljuZm1bA9lgVrYQsmKpsCkECPhs4wothZgR3/9LdrwUOJygNSyNoehCV2DAqeVVhSymgZE6KTVg1+ry7H+3ubdx9J3c/zN1fIqhmjI319VEhTh/70Eyq2D8cquRWgt6D8SVusWFU/hpLyoPeod8SlLI0SjKeWHJZ0LyUsVKdRCU12yJW8tY7rNquwpaBTfMrlduJoI1UNnCku0/2cHDUOIWZozE2an2ikfHzm9cyNo1boca1cvdsd3/J3c9x990Iqj8HE5RcdiG1wapjvWWvc/e7PddQHWHJ3ba0JYo918Zxbf+K0l/JWtjbtwdB28I5eWyvTvD6xK8XwILZaqYQ3DMWAAe7+9rivKa7T2XLvaltcV4rP2bWlKBqHuB/UcQgBVMyJ1GJjWj+nrtvNahpImHbn1iS9V2Sh40mqHa70P8+AGcsKcydcKQ0qCxB9TFATTPLs3ODBfPGNs+1f1F7iyA5SCMYZ+1wgoGUNxOUSuUllmCu8vzHBUy1NAi2VJ+3SLBPl3zWfxj+7B8OL7NNPBhN/2byaPCfhFj8c/LZ3oMtg2QXxidsKbk7ZhvOk5/pBNXArQneDw2A6bE2fB4MWLuY4AvWwQTP5QdPbVo52FLVXFKltyUmTLKnEHRyWkzQoSqlDg/bIPbFKivhXsVnMEHVdA5bj08ppYSSOSlxFkwufVa4mHsQ3dhYYYnEBorNJOi8UND19iIYl+xVd5+Ua/N34c+94/avR3DT/pOgXVQy5hLc5CFoI5iX6+Ku+UmS502JB7NdxJK2U9lSxTo5QdIcK11olsfgsZhZJ7aU7qUiNn7fDmbWMY/z9gby66n3KOHQNgTtL/NlcTMjWMGzicQS+VSqw2Ovz1aza8SNY1hoYenOy+HisESlcxbM3JDSHJnu/hsQm+VhWPjzvVy7TSPoTHJV3HKqYrOubNUpqSwL31+TCYY9+h7om+BLTyrn7Wpxg5vns8+ebOnVOzfRvsXBzM4iGDkA4KlwtAAphZTMSbGwYCqhS8xsp1i7MzOrb2YXEJQeVQLGufvbeRz+npkNMbMOcceaBVM0vUQwgCzATe6e5+jycXEYcB/Bt9q8BnWNDdNxQzhESVWC6tjqwFsJeiD+jbs7W6rujjKzu2KJUdhL9E62tDsbGlblFpdYdWp7grZe8evyMp9gwNc04Nmw2pWw9/EAgr9XoobleXL3b9hSAvm4me0enreKmZ1AMKdsng2q3X0+W0rRRpvZnXG9MTGzWmZ2kJk9yd9LCzpaMP3VhWbWJvbFILzmcWz5YHorhacyOfx5rQVTnsXek+0Jeh92Jugssi2uIHgtmhO06TsqfC8SXquNmV1K0P6vUz7nSCTW/i2/KtRpBWxPRqwX90mW4qTzpVWYOL8OdCTo3NTXkxjIO0knAd+b2b1mdkB8km5mjczsfIL3nhHM2fxIEV03ITNrbGbHmNmbBG1OjeD/+P9K4vpSSF4KBrvTo/w9gDPYMhjmJoIPqpy4dQ8C6fkc+13cflkEpWPr49Y5wQf9VoMG53Guc8ljYOK47dUJhmaIDTERG2T4D2C3Qjzv+EFRNxMMBLo5bt0N+Rx3HdswaHAe55sTd83fgOoF7D8gV5y/E7Qvc4I2O6dR8ICtp+SxbT/+PuDzH3HnfY2gZDa/QWgrAeNy/d1/z+O9NDnumIxc+8eGpIh/bh8RdPBI9rVsSNDwO/49uTb8PZugBDTPAXNJMMhuHtfpRpBUx//frIl7T8Ye3QvxfvhHrtcwPdf2Vrmuked7P9HzIeg4Ezt+I0EP9u+AJ1N5Pdgy+G3uwcSTGTR4q/dg3D4FDmqcxzH/zPXeXZXg8VyKf5Nbcr3mHr6vct/rfiGo1i3ofIUZNHh9XPw/5fFeyyK41ya8f+gR/UMlc1JcphPMQzmH4AZVg+BmOp7g2+3Znn+p1+UEyd5nBDeyOgQf3gsJvp3u4+4XeHhXyo+ZNSKokl1EcOPcigft5/oQ3Ah/I7iBTQV6eyGqFNx9KMFwKRMJPohrESQTkwhuyFsNdFxM4kvinvcCJup29xcIPiynEHxoVSb4IL6FYO7MlNo1xp33A4I2Za8RvL7pwNfAfwhKDfMt+fSgE8M5BINHP0VQxVWFIAFfSlCydypxw7AQlDIeR5AEziV479UJf/6PYJDXHh6OX5jkc/iZYLiW+9ky9ExmeP0e7v5Efsemwt0/JhhCZghBm8F1BFWWmQS9jG8A9nb3GYU4/fts6Sw0I/f/nrsvZUuTg9WFfO+/TfCl4P0w5uYEnQVKavDm4hD/GVmLxEPHpNoJZjDB/8Zogv+7FQRtdysRJFbTCN4Lbd39ncI/hYSqsyX+egTvuYUE40peArQI77UJ7x8SPSvg81BERERESjGVzImIiIiUYUrmRERERMowJXMiIiIiZZiSOREREZEyTMmciIiISBm2zdPklBWNGjXyHXfcMeowRERERAo0e/bsNe6e1HzNFSaZ23HHHZk1a1bUYYiIiIgUyMy+T3ZfVbOKiIiIlGFK5kRERETKMCVzIiIiImWYkjkRERGRMkzJnIiIiEgZpmROREREpAyLNJkzs0PMbKGZLTazKxPsN8DM3Mwy4tYNCY9baGYHl0zEIiIiIqVLZOPMmVk6cA9wILAcmGlmk9z9i1z71QYuBD6OW9ceGAjsDjQD3jGztu6+uaTiFxERESkNoiyZ6wosdvcl7p4FjAeOymO/kcDNwIa4dUcB4919o7t/CywOzyciIiJSoUSZzDUHlsUtLw/X/cXM9gJauvurqR4rIiIiUhFEOZ2X5bHO/9polgbcDpyR6rFx5zgHOAegVatWhQpSRCQzM5P333+fya+/zu+rV7MpMzPffavWrEnd7bbjiKOPpkuXLlSrVq0EIxWRiijKZG450DJuuQWwMm65NtABeM/MAJoCk8ysfxLHAuDu44BxABkZGVsleyIiecnKymLVqlUsmjePCePH89OKFXRo0oSBbdqwXfPm1KxcOd9j123axIrffmPi2LGM/fVXdth5Z44ZOJDW7drRtGlTKlWqMFNii0gJMfdochwzqwR8DRwArABmAie5+4J89n8PuMzdZ5nZ7sDTBO3kmgFTgDaJOkBkZGT4rFmzivZJiEi5snHjRr6cP5/nx41j6cKFtKhRg1O6daN906aEXypT4u7MXraMpz/5hJ+ysmjbqRMDzj6btu3aKakTkYTMbLa7ZxS8Z4Qlc+6ebWaDgLeAdOARd19gZiOAWe4+KcGxC8zsOeALIBs4Xz1ZRaSwNmzYwMQXX+SlJ5+kVmYmJ3fuTO8TTyxUAhfPzMho1YqMVq3Iycnh1fnzuen889lcty4nnnUWBx1yCJUTlPKJiCQjspK5kqaSORHJbcOGDdxz5518OHkyXRs35qyuXWlQo0axX3fl2rU88PHHzPv9dw4fMIDTzjxTSZ2I/E0qJXNK5kSkwnF3Pvv0U0YPGULv5s05MyODGhEkU39s3MidM2bw5fr1XHvrrbRp27bEYxCR0qlMVLOKiERhw4YNPPPII7zy5JPccsQR7NyoUWSx1K5alav79mXu8uVcdsYZnH7BBRw5YIBK6UQkJZqbVUQqjFWrVnHpWWfx9Rtv8Nypp0aayMXr1KIFz5x0ElP++1+uufhifvnll6hDEpEyRMmciJR7OTk5vP/uu5x33HH0b9SIG448kkrp6VGH9Tc1qlThngED2CMri3OOO45PZ82iojSDEZFto2pWESnX1q1bx7jbb2fW5Mk8ePTRNK5dO+qQEjq5Sxf222kn/nPhhRx+0kmcfNZZGnhYRBJSyZyIlFvLly/n3yefTM6CBTx18smlPpGLad2wIc+deipL3n6bS/71L37++eeoQxKRUkzJnIiUSx9//DHnnXgi5+++O5f17bvNY8aVtErp6Yw+4gj6N27MmQMG8OWXX0YdkoiUUkrmRKTcmfruu9w0eDAPH3MM3XbcMepwtsmh7dtz+4EHcvm55zJ37tyowxGRUkjJnIiUK++/9x53XncdDx9zDNvVqhV1OEVi50aNuO+II7h60CDmzZsXdTgiUsoomRORcuN/06Zx29ChPPyPf1C/evWowylSLevV4/7+/Rly3nnMV0InInGUzIlIuTB92jRuGTKEh489tkSm5IpCy3r1uKd/f64891zmf/551OGISCmhZE5EyrwZ06Zx8+DBPDJgAA1r1ow6nGK1Q/363HXkkVx13nnM/+yzqMMRkVJAyZyIlGmzP/mEm6+8kgePO45G5aSNXEFaN2zImMMOY+j557No4cKowxGRiCmZE5Ey6+uFCxl+8cXcffTRbFdGxpArKm2aNGFkv35cce65rFy5MupwRCRCSuZEpExasWIFl519Njcfeigt69ePOpxI7NGsGZfvuy8Xnnkmv/76a9ThiEhElMyJSJnz66+/MuiMMxjWsye7brdd1OFEar/WrTmrfXsGnXkm69evjzocEYmAkjkRKVPWr1/POaeeyqCOHclo1SrqcEqFQ3bbjSObNeOCs88mOzs76nBEpIQpmRORMmPTpk3835lnctLOO3NA27ZRh1OqDOzUia7Vq/OfQYPIycmJOhwRKUFK5kSkTHB3rhk8mO5163LM7rtHHU6pdHaXLjT+/XfuGDMm6lBEpAQpmRORMuG5p5/mz4ULOWvvvaMOpdRKM+PKnj2Z8+abTJk8OepwRKSEKJkTkVJv/rx5jL/vPm497DDSzKIOp1SrlJbGnUceydjrrmPZsmVRhyMiJUDJnIiUar///jvXXHwxYw47jKqVK0cdTplQr0YNhvXpw5Dzz2fDhg1RhyMixUzJnIiUWtnZ2Vx72WWc3K4dOzVqFHU4ZUqXVq3oVrcuY0aNUocIkXIu0mTOzA4xs4VmttjMrsxj+3lmNs/M5prZdDNrH67f0cwyw/Vzzez+ko9eRIrbs088QdrKlQzo1CnqUMqkQfvvzzcffsg7b74ZdSgiUowiS+bMLB24BzgUaA+cGEvW4jzt7nu4eyfgZuC2uG3fuHun8HFeyUQtIiVl3uef88JDD3HDYYdFHUqZZWbc3r8/d40erfZzIuVYlCVzXYHF7r7E3bOA8cBR8Tu4++9xizUBL8H4RCQia9euZdgllzDm8MOpUqlS1OGUaXWrV+faPn24Uu3nRMqtKJO55kD8V8Xl4bq/MbPzzewbgpK5C+M2tTazOWY2zcx6FG+oIlJSYu3kTtl1V7WTKyIZrVqxb9263DpypNrPiZRDUSZzeY0vsFXJm7vf4+47A4OBoeHqH4BW7r4XcCnwtJnV2eoCZueY2Swzm7V69eoiDF1Eisv4xx+n0qpVHNuxY9ShlCvn778/3378MZPVfk6k3IkymVsOtIxbbgGsTLD/eOBoAHff6O4/h7/PBr4Btprbx93HuXuGu2c0bty4yAIXkeIx7/PPmfDww1x/6KFRh1LuxNrP3T16NEuXLo06HBEpQlEmczOBNmbW2syqAAOBSfE7mFmbuMXDgUXh+sZhBwrMbCegDbCkRKIWkWLxxx9/MOySS7jtiCPUTq6Y1KlWjev69mXIoEFs3Lgx6nBEpIhElsy5ezYwCHgL+BJ4zt0XmNkIM+sf7jbIzBaY2VyC6tTTw/U9gc/N7DPgBeA8d/+lhJ+CiBQRd2f4kCGc2K4drRs2jDqccm3vli3pVq8eY2++OepQRKSIRPr1191fB17PtW5Y3O8X5XPcBGBC8UYnIiVl0sSJbFq6lOMOPzzqUCqEf++3H/+cMIEZM2bQvXv3qMMRkW2kGSBEJFK//PILD40dy8h+/TDNu1oiKqWlcdMhh3DTsGFkZmZGHY6IbCMlcyISGXdn6GWXcWGXLtSpVi3qcCqU7WvX5vi2bbl++PCoQxGRbZR0Mmdm1YszEBGpeN564w3SfvyRfrvsEnUoFdKJHTvy3cyZfDp7dtShiMg2SKVk7gczu8/M9i62aESkwli7di333HQTIw86SNWrEUlPS2P0QQcxasgQzQ4hUoalksx9AJwFfBJObj/IzOoVU1wiUo65OyOGDOGsPfekfnUV+kepVf36HNSsGXeqd6tImZV0MufuhwE7AMMI5km9E1hpZk+ZWZ9iik9EyqH3p05l7aJF9O/QIepQBDh7n32YPWUK8+fNizoUESmElDpAuPtKdx/t7m2AA4AXCWZleMfMvjGzq8ysWXEEKiLlw9q1a7ltxAhuOPRQVa+WEulpaYw++GBGDh6s6laRMqjQvVndfaq7nwI0A54CWgMjge/M7CUz61pEMYpIOeHujBk5kuPatqUC5ujzAAAgAElEQVRxrVpRhyNxdmnUiL3r1OGRe++NOhQRSVGhkzkza2RmlwAzgFOAP4H/Ag8CfYEPzOzsIolSRMqF2TNnsmTWLE7JyIg6FMnDpb168c6LL/LNN99EHYqIpCClZM4Ch5jZ88ByYAywEfg30Mzdz3L384FWwHvANUUcr4iUURs2bODGa65h9KGHRh2K5KNSejrX9O3LyMGDyc7OjjocEUlSKuPMjQC+B14DDgYeA7q4+97ufr+7/xHb193XhtubF3G8IlJGjbvrLvZv1Igd6tePOhRJYK8WLWi6aRMvPf981KGISJJSKZkbCvwInAds7+7nunuikSY/BUZsS3AiUj4sWbKE9155hUE9ekQdiiRh2IEH8vi997JmzZqoQxGRJKSSzHV29y7u/qC7/1nQzu6+wN01T4xIBZednc21l1/OsD59qJSmGQTLghpVqnBBly4MHzIEd486HBEpQCp31tvM7ID8NppZHzN7twhiEpFy5IVnn6UV0Km5Wl2UJQe2a0fW8uVMmzo16lBEpACpJHO9ge0SbG8C9NqmaESkXPn55595atw4ru6jccXLGjNj5IEHMmbUKDIzM6MOR0QSKMo6j3oEPVtFRAAYNngwF3XtSo0qVaIORQqhSa1anNCuHTeOHBl1KCKSQKVEG81sT6BT3KoeZpbXMQ0Ihif5oghjE5EybMb06WSvXEnfLl2iDkW2wcCOHTn1hRf4+uuvadu2bdThiEgeLFHjVjO7Frg2XHQg0dw7fwAnuPubRRde0cnIyPBZs2ZFHYZIhZCVlcXAI4/krn79aF63btThyDaa/8MP3PT55zz63HOkp6dHHY5IhWBms909qRHWE5bMAY8SDP5rwLvA9cDkXPs4sA74wt01qZ+I8OhDD7Fvw4ZK5MqJDttvT9NPP+X1V17hyKOPjjocEcklYTLn7t8TDBSMmZ0JvO/u35ZEYCJSNq1Zs4ZXx4/nhYEDow5FitDQAw7gtDvuoO+BB1KzZs2owxGROEl3gHD3x5TIiUhBbrj2Ws7r3JkqlQoq+JeypG61ahzZujX33H571KGISC753m3N7LTw1yfc3eOWE3L3x4skMhEpc+bNm8dPX33FoccfH3UoUgzO6NqVE555huVnnEGLFi2iDkdEQvl2gDCzHIL2cNXdPStuOVEnCHf3Utk6Vh0gRIpXdnY2px17LNd17Urbxo2jDkeKyfQlS3jqhx+499FHMUv0cSAi26KoOkD0AXD3rPhlEZG8vDJxIq3MlMiVc/vvtBOPzZnDhx98wH7du0cdjohQwNAkxX5xs0OAO4B04CF3vzHX9vOA84HNBD1mz3H3L8JtQ4B/hdsudPe3El1LJXMixWfdunWcdMQRPPmPf1CnWrWow5FitnztWi6eMoWnJ02iigaEFikWqZTMFckMEGZWtRDHpAP3AIcC7YETzax9rt2edvc93L0TcDNwW3hse2AgsDtwCHBveD4RicBdY8ZwbJs2SuQqiBZ167JX3bo888QTUYciIqSQzJnZoWZ2Xa51/zaz34E/zexpM6ucwrW7AovdfUlYlTseOCp+B3f/PW6xJkGbPcL9xrv7xrCH7eLwfCJSwpYuXcqsd9/l5L33jjoUKUH/6dmTFx57jN9++y3qUEQqvFRK5i4Hdo0tmNluBFWkKwkGEj6BoEo0Wc2BZXHLy8N1f2Nm55vZNwQlcxemcqyIFK+cnBxGX301l3XvTqW0opzqWUq7apUr88+OHbl5xIioQxGp8FK5++4GxDc6OwHIBLq6+6HAs8DpKZwvr25QWzXgc/d73H1nYDAwNJVjzewcM5tlZrNWr16dQmgikowPZszA1qxh3x13jDoUicBRHTrw3dy5fPXVV1GHIlKhpZLM1QfWxC33A96Nqwp9D2idwvmWAy3jllsQlPLlZzwQm0cmqWPdfZy7Z7h7RmP1sBMpUllZWYwdNYphfftGHYpEJM2Mq3r14vqhQ9m8eXPU4YhUWKkkc2uAHQDMrDbQBZget70yQa/UZM0E2phZazOrQtChYVL8DmbWJm7xcGBR+PskYKCZVTWz1kAb4JMUri0i2+ipxx6jS4MGNNP8qxVah+23p/HGjbz9VsIBBUSkGKUy386HwHlmtoCgB2ol4PW47bsAPyR7MnfPNrNBwFsESeAj7r7AzEYAs9x9EjDIzPoBm4BfCatxw/2eA74AsoHz3V1fC0VKyG+//cZLTzzBcyecEHUoUgpcfcABnDlmDH369qWaejSLlLikx5kLhwOZCsTqKx9z9zPDbQZ8C0yNrSttNM6cSNG56rLL6JqVxdEdOkQdipQSd3/wAb7nnlxw6aVRhyJSLhTLOHPhYL27EQwL0jtX0lYPuB0Ym0qgIlL2fPPNNyyZM4cj2+ceFlIqsnO6dWPKpEn8/PPPUYciUuFEOgNESVLJnMi2c3f+dfLJXNCmDXs112hA8ndvLFzIlKwsbr3rrqhDESnzin0GCDOrYWYtzaxV7kdhziciZcNHH35I1d9+UyIneTqoTRtWfPEFixcvjjoUkQollRkg0szsSjNbAfwBfEfQTi73Q0TKoezsbMaOHs2VvXpFHYqUUulpaVzevTs3DBtGRan1ESkNUunNeiNwGbAAmACoYYRIBTJp4kR2qVaNHerXjzoUKcU6t2hB5Vmz+OjDD9l3v/2iDkekQkglmTsFeNPdDyuuYESkdMrMzOSxe+/l8aOOKnhnqfCu6t2by0aPpsvEiVSqlMrHjIgURqozQEwsrkBEpPR65IEHOKhlS+pqDDFJQqt69WhTrRqvvPxy1KGIVAipJHPzgO2LKxARKZ1+/fVX3n7xRc7q2jXqUKQMuaJnTx699142bNgQdSgi5V4qydxwghkgWha4p4iUG7eOHs2ZHTtSVdVlkoK61atzYMuWPHTffVGHIlLupXJ33hv4HvjCzF4i6Lmaewotd/eRRRWciETru+++Y9Hs2YzQtF1SCGd368bx48dz0umn06BBg6jDESm3UpnOKyeJ3dzd07ctpOKhQYNFUuPu/N8ZZ3B68+bsu+OOUYcjZdTL8+Yxu1o1Rt5yS9ShiJQpqQwanErJXOtCxiMiZdDcuXPJ+uEH9u3ePepQpAw7cvfdeerZZ/n+++/ZYYcdog5HpFzSdF4ispXNmzdz6rHHMqJrV3Zp1CjqcKSM+/C773hi5UruffTRqEMRKTNKYjqvXcysu5nVLczxIlK6TZk8me1ycpTISZHYZ4cdyFyxgs8++yzqUETKpZSSOTM7wsy+ARYC7xN0isDMmpjZYjMbUAwxikgJ2rRpE/fddhtX9e4ddShSTpgZV/XuzS3XXUdOTjLNr0UkFanMzdobeAn4hWCYEottc/efgG+AgUUcn4iUsGeefJIuDRrQuFatqEORcqRN48Y0ys5myjvvRB2KSLmTSsncMOAzoBtwTx7bPwQ6F0VQIhKNP//8kxcee4yL1OlBisFVffpw/5gxbNq0KepQRMqVVJK5DOApd8+vjHw50HTbQxKRqNw9dizHtGlDzapVow5FyqEmtWqxd/36PDd+fNShiJQrqSRz6cDGBNsbAVnbFo6IRGX16tV8OHkyp3RWAbsUnwu7d+e5Rx4hMzMz6lBEyo1UkrkvgR4Jth9BUA0rImXQzSNGcO5ee1E5vVSO+y3lRK2qVTlql1245447og5FpNxIJZl7GBhgZv+KO87NrIaZ3QnsC4wr6gBFpPh9++23LFuwgIPatYs6FKkATuncmelvvsmvv/4adSgi5ULSyZy73wc8CzwILAIceAZYCwwCHnX3p4ojSBEpXjcMG8Z/9tuP9LRCDT0pkpIq6en8s2NHbhk1KupQRMqFlO7c7n4KcCwwBfiKYJiS14Hj3P1fRR+eiBS3OXPmsPmnn8ho2TLqUKQCOXy33Vg8Zw5Lly6NOhSRMi/lr+Hu/pK7H+vuu7t7e3c/yt0nFObiZnaImS0MBxy+Mo/tl5rZF2b2uZlNMbMd4rZtNrO54WNSYa4vUtHl5ORw68iRDO7ZEzMr+ACRIpKelsaFXbty0/DhUYciUuZFVqdiZukE49UdCrQHTjSz9rl2mwNkuPuewAvAzXHbMt29U/joXyJBi5Qz702dSqNNm2jbuHHUoUgF1L11a9YtXcqCBQuiDkWkTEsqmTOzumZ2lZnNMLPVZrYx/DndzK40szqFuHZXYLG7L3H3LGA8cFT8Du4+1d3Xh4sfAS0KcR0RyUN2djb33norQzRtl0TEzLiiRw9uHj4cd486HJEyq8Bkzsz2BBYAIwl6rFYBfgp/7gdcD8zPo1StIM2BZXHLy8N1+fkX8EbccjUzm2VmH5nZ0SleW6TCm/jii+xeqxZNa9eOOhSpwHZv2pSaf/7JBzNmRB2KSJmVMJkzs2rABKAxQdLW2t3runtLd68LtA7Xbwe8aGapDBufVwOdPL+amdkpBDNQ3BK3upW7ZwAnAWPNbOc8jjsnTPhmrV69OoXQRMq3jRs38vgDD3Bpj0RDR4qUjCt79uTOG24gOzs76lBEyqSCSuYGAjsDJ7n7Ne7+ffxGd//e3YcCpwBtw/2TtRyI7z7XAliZeycz6wdcDfR3979moHD3leHPJcB7wF65j3X3ce6e4e4ZjdUmSOQvjz70EH2bN6dutWpRhyJCq/r12alqVd58/fWoQxEpkwpK5voDnxTUW9Xdnwc+IVebtwLMBNqYWWszq0KQCP6tV6qZ7QU8QJDI/RS3vn6sFNDMGgHdgS9SuLZIhfXHH3/w2nPPcU63blGHIvKXy3v25OG77mLTpk1RhyJS5hSUzHUE3k7yXG+H+yfF3bMJBht+i2CqsOfcfYGZjTCzWO/UW4BawPO5hiDZDZhlZp8BU4Eb3V3JnEgS7hozhhN2243qlStHHYrIXxrUqMG+jRvz5GOPRR2KSJlTqYDtjYFkR3RcGu6fNHd/nWDQ4fh1w+J+75fPcR8Ae6RyLRGBn376iVnvvcflJ5wQdSgiWxm0334MfPJJTjjpJGrUqBF1OCJlRkElczWB9QXsE5MZ7i8ipdTNI0dyzt57Uzk9PepQRLZSo0oVjmnThnvvuCPqUETKlIKSOQ0JL1JOfPvttyz/4gsObNMm6lBE8nVy585Mf+stfv3116hDESkzLNFAjWaWQzALw4okztUc6OTupfIrf0ZGhs+aNSvqMEQic+5pp/Gvli3pusMOBe8sEqFJCxbwUeXKXH/rrVGHIhIZM5sdDsFWoILazEEw5MdWw37kQ0N4i5RCc+fOZdOPP9Kle/eoQxEp0GG77cYTzz7LsmXLaNmyZcEHiFRwCatZ3T0txUepLJUTqchycnK4dcQIBvfogZlaTkjpVyktjYu6dePG666LOhSRMiGpuVlFpOx6f9o0GmzaRLsmTaIORSRp3Vu35o+lS/niC406JVIQJXMi5Vh2djZ333wzQ3r1ijoUkZSYGVf06MFN111HorbdIqJkTqRce/nFF2lfqxbb16kTdSgiKevQtCk11q1jxowZUYciUqopmRMppzZs2MATDzzAf3r0iDoUkUIb0qsXd95wA9nZ2VGHIlJqKZkTKaf+++CD9GvZkrrVqkUdikihtapfn12qVeO1V1+NOhSRUkvJnEg59Pvvv/PmhAmc1aVL1KGIbLPLe/TgkbvuIisrK+pQREolJXMi5dDYm2/m5N13p3rlylGHIrLN6teoQa9mzXjskUeiDkWkVEo6mTOzyWZ2gplVKc6ARGTbrFq1is9mzOAfe+wRdSgiRea8bt14Zfx41q1bF3UoIqVOKiVzewNPAyvNbKyZ6ZNCpBS6cfhw/p2RQaU0FbxL+VGjShWO33VX7hgzJupQREqdVO72TYGTCeZqvQCYa2Yfm9nZZlarWKITkZQsWrSINYsX02eXXaIORaTIndCxI7OmTmX16tVRhyJSqiSdzLl7lruPd/cDgZ2AUcB2wAPAD2b2sJlp4keRCN1w7bVc1r07aZq2S8qhyunpnJeRwY3Dh0cdikipUqh6GHf/3t2vBVoDhwBTgTOA983sCzO7yMxqFl2YIlKQjz/+mCq//UbH7bePOhSRYtNvl11Y+dVXLFmyJOpQREqNbW1U0wnoD/QADPgGyAFuBxab2X7beH4RSUJOTg63jRrFlT17YiqVk3IsPS2NS/fdl+uHDYs6FJFSI+Vkzszqmdn5ZvYpMAs4C3gL6Ofubd29A9APWA/cU6TRikieXn/tNVpXqcKODRpEHYpIscto0QJ+/pmZM2dGHYpIqZDK0CR9zewpYCVwF1ADuAJo7u4D3f3d2L7h7zcCuxdxvCKSy6ZNm3jozju5fP/9ow5FpESYGVf17Mlto0aRk5MTdTgikUulZO4d4B/AS0Afd9/V3ce4+8/57L8Y0OzIIsXs8f/+l/23246GNdVMVSqOnRo2pLkZb731VtShiEQulWTuPwSlcCe7+7SCdnb3qe7ep/ChiUhB1q1bx8Snn+bf++wTdSgiJW5wz56Mu/12Nm3aFHUoIpFKJZmrDTTLb6OZ7W5mapEqUoLuHDOG43bdlRpVNDGLVDyNa9Wia8OGPP3EE1GHIhKpVJK5a4E9E2zvEO4jIiXgp59+YubUqQzs2DHqUEQic1H37kx4/HHWr18fdSgikUklmStovINqQHYqFzezQ8xsoZktNrMr89h+aThu3edmNsXMdojbdrqZLQofp6dyXZHy4KYRIzhv772pnJ4edSgikalRpQrHtGnD3bffHnUoIpFJmMyZWR0za2VmrcJVDWPLuR6dCKb6Wpbshc0snWDokkOB9sCJZtY+125zgAx33xN4Abg5PLYBQSlgN6ArcK2Z1U/22iJl3eLFi1n55Zcc2LZt1KGIRO6Uzp354O23WbNmTdShiESioJK5S4Bvw4cDY+OW4x+zCcaWuz+Fa3cFFrv7EnfPAsYDR8XvEHaiiJWdfwS0CH8/GJjs7r+4+6/AZIKZKETKPXfn+muu4XJN2yUCBNN8nbv33prmSyqsSgVsfy/8acAwgmFJPs+1jwPrgI/c/YMUrt2cv5fkLScoacvPv4A3EhzbPIVri5RZM6ZPp+ratXRu0aLgnUUqiIPbteOJ55/n66+/pq1KrKWCSZjMhUOQTAMI26vd7+4fF9G18ypS8Dx3NDsFyAB6pXKsmZ0DnAPQqlWrrQ4QKWuys7O544YbuK1376hDESlV0sy4Yv/9uX7YMP77zDOa1k4qlKQ7QLj7mUWYyEFQmtYybrkFwewSf2Nm/YCrgf7uvjGVY919nLtnuHtG48aNiyxwkai88PzzdKhdm5b16kUdikip06lZM2qtW8f70wocClWkXMk3mcvV8YF8Oj5s9Ujh2jOBNmbW2syqAAOBSbli2At4gCCR+ylu01vAQWZWP+z4cFC4TqTcWr9+PU+PG8cl3btHHYpIqXVV797ceeONZGenNLiCSJmWqJr1OyDHzGqEHRS+I59q0FySGifB3bPNbBBBEpYOPOLuC8xsBDDL3ScBtwC1gOfDIvOl7t7f3X8xs5EECSHACHf/JZnripRVY2+5hQHt2lGnWrWoQxEptZrVqUNGgwY8/cQTnHbmmVGHI1IizD3v/MzMriNI3ka6e07cckLuXiq7E2VkZPisWbOiDkOkUFatWsX5J57IM8cfTxWNKyeS0J9ZWZz4wgs889pr1NScxVJGmdlsd89Iat/8krnyRsmclGWDzjmHY+vVo88uu0QdikiZ8MzcuXzdoAHXjhoVdSgihZJKMpfKDBAiEoHPP/+cdd9/T6+dd446FJEyY8AeezDvgw9YsWJF1KGIFDslcyKlWE5ODjdeey1X9eypAYJFUlA5PZ2Lu3Vj5NChUYciUuwS9WbNMbPNKT7UfUikCL3x2mu0MKOthtYRSdl+O+7Iph9+YPbs2VGHIlKsEvVmfZzkeq+KSDHIyspi3B138Mjhh0cdikiZlGbG1b16MWT4cJ55+WXS0lQZJeVTvsmcu59RgnGISC4P3ncfB7ZsSUP1xhMptJ0aNmTnKlWY9PLLHP2Pf0Qdjkix0NcUkVLo119/5e0XX+SsLl2iDkWkzLu8Rw8euftuNmzYEHUoIsVCyZxIKXTD8OH8a6+9qFYp4fTJIpKE+tWrc3jr1tx3111RhyJSLBJ1gPjWzL4xs8rh8pIkHt+UXOgi5dOiRYtYPn8+h+26a9ShiJQbZ+y9N9Nee401a9ZEHYpIkUtUMvc9sJQtnSCWhusSPZYWW6QiFUBOTg6jhg7liv33p5Iaa4sUmaqVKvHvjAxGDxsWdSgiRS5RB4jeiZZFpOhNffdd6vz5J52aNYs6FJFyp1+bNjzx/PPMnz+fDh06RB2OSJHRV3+RUmLjxo3cdeONDO3TJ+pQRMqlNDOu7t2b64cOJTtbw6JK+ZFyMmdmVc3sYDP7v/BxsJlVK47gRCqScffcQ9/mzdmudu2oQxEpt3Zt0oQd09KYOGFC1KGIFJmUkjkzOw1YAbwO3BM+XgdWmNkZRR6dSAWxatUqpkycyHn77BN1KCLl3pW9e/Povfeybt26qEMRKRJJJ3NmdgLwKLAOuBo4GjgGGBquezjcR0RSNHzIEC7p1o0q6elRhyJS7tWpVo2TO3Tg5lGjog5FpEikUjJ3FfAVsKe73+juk9x9orvfAOwJLCJI8kQkBR988AGbf/yRnjvvHHUoIhXGgD324OuZM1m0aFHUoYhss1SSuXbAf93999wb3H0t8F+gTVEFJlIRZGdnc8vw4VzTuzdmFnU4IhVGpbQ0rurZk+FDhpCTkxN1OCLbJJVkbhWQ6NMmB/hx28IRqVgevP9+ejRtSst69aIORaTC2XP77WmWk8Orr7wSdSgi2ySVZO5R4Awzq5V7g5nVAf5JUDonIklYs2YNb06YwP917Rp1KCIV1pU9e/LgHXeQmZkZdSgihZZoOq+e8Q/gfWA9MM/MLjezI83sCDO7AviMoBPE/0ombJGyb/jVV3NBly5Ur1w56lBEKqwGNWpwwq67csv110cdikihJZrF+z22TOUVE6tmvSluW2zdDsBkQN3xRAowc+ZMMpcto89ee0UdikiFd/wee3DqhAl8++23tG7dOupwRFKWKJk7s8SiEKlAsrOzuXHYMMb07k265l8ViVyV9HSu7N6dYVdcwePPPafOSFLmJJqb9bGSDESkohh3333s17gxO9avH3UoIhLaq3lztp83j0kTJ3LU0UdHHY5ISiItFjCzQ8xsoZktNrMr89je08w+NbNsMxuQa9tmM5sbPiaVXNQihffTTz/x1oQJnK+ZHkRKnSG9evHQHXewfv36qEMRSUmiatY8mdl2QAZQnzySQXd/PMnzpBNMB3YgsByYaWaT3P2LuN2WAmcAl+Vxikx375Ra9CLRum7IEC7u2pVqlVL+1xORYla/enVO2m03bho5kuE33BB1OCJJS/oTxczSCJKvs0hcopdUMgd0BRa7+5Lw/OOBo4C/kjl3/y7cphEdpcybPn06m1aupLeGIhEptY7bc09Oef55Fi5cSLt27aIORyQpqVSzXgacCzwDnE7Qi/VK4HyCqbxmEZSyJas5sCxueXm4LlnVzGyWmX1kZmrgIKVaVlYWY0aMYHjfvmpcLVKKVUpL45pevRg5ZAibN2+OOhyRpKSSzJ0OvOXupwFvhOtmu/v9wN5Ao/BnsvL6RMs9FEoirdw9AzgJGGtmW01saWbnhAnfrNWrV6dwapGi9cDdd9O7aVOa1a0bdSgiUoDdmzallTsvT5gQdSgiSUklmduJLUlcrNqzMoC7/0kw+8NZKZxvOdAybrkFsDLZg919ZfhzCcGYeFsN2OXu49w9w90zGjdunEJoIkVn2bJlTHn5Zf69775RhyIiSRrSty+P3nMPa9eujToUkQKlksxlApvC39cRlKI1idu+ir8nZwWZCbQxs9ZmVgUYCCTVK9XM6ptZ1fD3RkB34traiZQWOTk5DLv8cob06EHldI2nLVJW1K5albM7dWL4VVdFHYpIgVJJ5r4HdgZw903AYuCQuO39gB+TPZm7ZwODgLeAL4Hn3H2BmY0ws/4AZtbFzJYDxwEPmNmC8PDdgFlm9hkwFbgxVy9YkVLhpRdfpHFWFt122CHqUEQkRUe0b8/vS5Ywffr0qEMRScjck2umZmZjgKPdfedweSgwAphG0P6tB3Cruw8upli3SUZGhs+aNSvqMKQC+eWXXzj9mGN46thjqVOtWtThiEghrPz9d8574w2ef/11qlatGnU4UoGY2eywb0CBUimZuxX4d6x6E7gBuBvoCOwOjAOuTSVQkfLs6ssu48KuXZXIiZRhzerU4fh27Rh13XVRhyKSr6STOXf/wd3fcveN4fJmd7/Q3Ru4e2N3/z9331B8oYqUHW+8/jqV16zhgF12iToUEdlGA/fck+8//ZRPP/006lBE8qRZvkWK2Lp167jn5pu5tm9f0jSmnEiZVyktjeF9+jByyBCysrKiDkdkKyknc2Z2vJk9Y2Yfh49nzOz44ghOpCwaesUVnLPXXjSsUSPqUESkiLRu0IBDW7XiVk3zJaVQ0smcmdUws8kEM0CcALQB2oa/P2NmU8ysZvGEKVI2TJs2jczvv+dwTQMkUu6c2bkz8/73PxYsWFDwziIlKJWSueuBA4C7gGZhW7n6QLNwXR9gdNGHKFI2ZGZmcuvw4Yw44ADS09SCQaS8qZyeznV9+nDtFVeQnZ0ddTgif0nlE+cE4Hl3v9jdV8VWuvsqd78YmBDuI1IhDb/mGk5p357tatWKOhQRKSbtGjemR5Mm3D12bNShiPwllWSuDsEAvfl5N9xHpML55JNP+HH+fI7t0CHqUESkmJ3XpQszXn+db775JupQRIDUkrnPCdrJ5acNMG/bwhEpe7Kyshh99dWMPOAAKql6VaTcq1qpEsN69eLq//yHzZs3Rx2OSErJ3FDgbDM7MvcGMzsKOAvQJHZS4Vw/YgTH7LwzLerWjToUESkhe2y/PR1r1j4/jEQAACAASURBVOShceOiDkWESvltMLNH8lj9LfCymS0kmE/VgfZAO4JSuZMJqltFKoQ5c+aw6KOPuPrYY6MORURK2CXdu3Pis89yyGGHsYPmX5YI5Ts3q5nlFOJ87u7p2xZS8dDcrFLUMjMzObF/f8b268eO9etHHY6IRGDO8uXcOn8+jz33HJUq5Vs+IpKyIpmb1d3TCvEolYmcSHG4ccQIjmzVSomcSAW2V4sWtK9ShQfvvTfqUKQCU2ttkUKYOmUKy2bP5syuXaMORUQidkWvXrz74ovMnz8/6lCkgirMdF5mZp3NbED46GymCSil4vjll1+4dfhwbjn0UM29KiJUTk/n5kMOYejFF5OZmRl1OFIBpZTMmdkhwDfATODZ8DETWGxmBxd9eCKlS05ODpdfcAH/2WcfGtbU7HUiEmjdoAED27XjmsGDow5FKqCkW2uaWXdgEvAncCcQK0/eHTgDmGRmfdz9g6IOUqS0eOShh2iRnU3fXXaJOpTIbdy0iUHjxzPlq6/46Y8/2L5uXc7v1YuL+/WLOjSRSBy/555Mf/VVXp00iSP69486HKlAUul6MwxYBXRz9x/iN5jZLcDH4T6HFF14IqXHV199xZvjx/PkgAFRh1IqZOfk0LROHd6+6CJ2atSIz1es4OA77mD7unU5oUuXqMMTKXFpZozq149Tb7uNjK5dadq0adQhSQWRSjVrN2Bc7kQOIFz3ILBPUQUmUppkZWUx+KKLGN23L9U0/AAANatWZeRRR7FLkyakpaXRqWVLDt9jD2ZoiiOpwOpVr85V++/PfwYNIienMCN8iaQulWSuCvBHgu2/h/uIlDvXDBnCgDZtaNekSdShlFrZmzczffFi9mzRIupQRCK1T8uWdK5dm7G33RZ1KFJBpJLMfQkMNLOtiiXCdSeE+4iUK6+9+irrFi3ixA4dog6lVLvw2WepW706p+2jAnqp2MyM87t04dPJk/nkk0+iDkcqgFSSufsIqlqnmNnhZtY6fBwBTAm3adREKVdWrFjB/bfeyqi+ffn/9u47uop6C/T4d6dCgIQWei/hEZBLR5Heq/SiWK4iIsUQQBDxCqIieKVL8XIFBASDNIVHEaQERXq7lFAiHZQgJRCBtPN7f+TACymQwEkmJ9mftc5a58z8ZmZnOMlsftXNJWtNy/ifbdsoPXIkhYYNY/qWLY8sO3TpUn4NDWVdQAAe2gytFNnc3BjfrBmfjBjB7duPatRS6uml+OlkjPka+AKoR9yo1lD760f7ti+MMXPSIkilrBATE8OQ/v0ZVb8+eby8rA4nXc3eto23Fy3i4o0b3L53j3eCgth47FiSZQOXLGHDsWNsGjyY/DlzpnOkSmVcxXx86F+tmvafU2kuVVUNxpj3gIrACOA/wGzgPaCiMWaE48NTyjqff/op9fLmpVbx4laHku5m//ILALN69WL1gAEAfLNjR6JyAUFB/Hz8OJuHDME3V650jVEpZ9DKz48Cd+8y7+uvrQ5FZWIpag8REU/imlH/MMacJK6G7qnZJyGeCrgCXxtjxifY3wCYAlQBehpjlsXb9xrwL/vHT40x8x0Rk1IAwVu2cGr7dr7u0sXqUCxx4soVABqWL0/p/PmZ99prlEsw+OPctWt8uWULnm5ulP7ggwfb65crx7qAgHSNV6mMSkT4V8OGvLx4Mc8+/zyVKlWyOiSVCYkx5vGF4gY43AWGGmOmOeTCIq7ASaA5cJG4lSReNMYci1emFOANvAusup/MiUheYC9QEzDAPqCGMeZGcterWbOm2bt3ryNCV5nc1atXeb1LF+Z36pQlV3mItdlw69cPgOuTJpEnC94DpRztzPXrDP75Zxb9+CM59HdKpYCI7DPG1ExJ2RQ1sxpjYoibMNiRC1HWBkKNMaeNMVFAENAhwXXPGmP+ByTsbNAS2GiMuW5P4DaikxUrB4iOjmZo//6899xzWTKRA7h9796D97myZUu3624+fpwGX3xB3sGDkb59GbVqFUcuXcKtX79k++s9zg8HD+LRvz+n7DWNKVVq5EgaTZz4RNdUKiml8+bl5QoVGDlkiPafUw6XmmFnS4HuIvKlMcYR38SiwIV4ny8S15T7pMcWdUBMKosbN2YMNby8qF+2rNWhWOZ+MpfN3R03V9d0ueaJP/+k1bRpVCtenPGdOuHl4UHdsmV5e9Eini9blub+/k903o5Vq/JM0aK8t2IFK+y1jc7syq1bjF69mjWHD3Pl1i0KeXvTqVo1xrRvT+4kBulI375JnieHpycR01LfyHInKopKH33E2WvXGNCoEdNffPHBvoh79xi6bBk/HDwIQOdq1ZjQtSs5PD0fOsfKAwd4ee5cjo4eTan8+VMdgzPrUqUKBzZuZPasWbxt74uqlCOkJpn7GmgMbBSRKcAp4E7CQsaY8yk8X1K1fI9v803FsSLyFvAWQIkSJVJ4apVVLVu6lCuHDvFB27ZWh2KpiMhIAHImeAinpTnbtxMdG8vSvn0pkTcvADt+/52NISH88JRJ2KAmTXjtm284evkylYoUcUS4lgi7dYs648dz+eZN+tavT+WiRTly6RKzgoPZduoU24cPx8sj8bzt9cuV46369R/a5v6ESfqoVav4KyIiyX3vrVjB4t27eb9VXCPJuPXrcXNx4ct4CV/43bsMDArikxdeyHKJHMT1nxvdtClvrFiB/zPP0KBBA6tDUplEapK5I8QlTAI0ekS5lP6VuAjEHyZYDLicimPjx1AM2JqwkDFmNnEjbqlZs2ZKE0WVBR08eJDvZs7km86dcc1i88kldL9mLj2bWH8NDaV8gQIPEjmAmcHB5MuRgzbPPPNU5+5crRr9Fi/mq+DghxILZ/PZunWcu3aNxb1782Lt2g+21y1blpfmzGHSxo38K4n/iJTx9eVlB0zkvP/8eaZs2sS/O3dm6LJlifavOHCAoc2bM7JNGwAiY2L4evv2h+75eytWUNjbm0FNmz51PM7Kw9WVKW3a8PqHH1Ji/nxKlSpldUgqE0jNU+tj+2tMvPdJvVJqD1DePvGwB9CTuPnrUuInoIWI5BGRPEAL+zalUu3KlSv8KzCQKa1bkysda6MyqvRM5kavWoX07cuO06c5FRaG9O2L9O3L0n37+OHgQZr7+yeqRbobFUWx996jxIgRREZHP7TvzQULcH37bYL27HmwLWe2bNQvV46l+/cnuv6F69fpPns2PoMG4T1oEO2nT+f3q1cTlUvtNdPClpMnye7uTs9atR7a3qNmTbK5uzPvt9+SPTYqJoaIeH0hUyvWZqPPwoW0qlSJztWqJVnmbnQ0eeP1M82bIwd/22t5IS5hn7t9O/995ZUs/x+m/DlyMK5pUwL69CEimZpOpVIjxTVzxpiPHHlhY0yMiAwkLglzBeYaY46KyMfAXmPMKhGpBawE8gDtRWSMMaaSMea6iHxCXEII8LEx5roj41NZQ1RUFP3feIN/1atH8dy5rQ4nQ7jfzJoeiW3rypXJ6enJ8BUreLFWLdrYl0wrkTcvEZGR1E6i1iK7hwdj2rfnzYULmRkczOBmzQB4f+VK5mzfzowXX0yU8DxXpgw/HTvG8T//5P8UKgTAzTt3aDBhAhdu3ODtBg3wL1yY4JMnaTxxIncTJGxPcs37bDYb1+8k6pGSrLxeXrgkkexERkeTzd0dkYd7mbi4uJDd3Z3Tf/3FXxERiSZuXrZ/P9/u2kWszYZvrlz0qFGDTzt2xCd79hTHNPnnnzn+558sT6YPHsTd46+2baNh+fIYYFZwMHXtfU+jYmLos3Ahg5s2pZp2eQGgcqFC9K1ShYFvvcWchQtxTaf+qSpzSuk8c75AGeAvY8zvjrq4MWYtsDbBtlHx3u8hrgk1qWPnAnMdFYvKeowxDB4wgC6lS/OsPmAeuF8zlx595p4tU4bLN28C0KtOHdram1Tnbd8OQFlf3ySP+2fdukzetIlx69fTp149vv71V8avX8+Y9u3p36hRovL3z3P08uUHydy/f/qJs9euMffVV3n9+ecB6N+oEYFLljB18+anvuZ9569ff2gevsc5M3Zskv3JKhUpwokDBzh44QJV401kffDCBW7Yk8Xz168/lMzVLlWKbjVqUK5AAW7dvcvaI0eYvnUrwadO8dvw4eRMQe3rmb/+YvTq1Yxq25ZS+fNz9q+/kiw3pXt32s+YQdVPPwWgfIECTOneHYCxa9cSFRPDR+3bp/g+ZAVt/PwIvX6dj0eNYszYsVaHo5zYI5M5EXEhbr3VN7EPOhCRHUAnY0zitgilnMiUiRMpGBFBz5opmsYny7h9v2YunfrM7T8fN2aqeryE+qq96SlvMtPDuLq4ML5TJ9rPmEHHWbPYfOIE7zRuzKh27ZIsn8+e4ITFWyPzh0OHKOjtzavPPfdQ2fdatUoymUvtNe8r5OPDxsDAR5ZJWD4pgU2b8sPBg3SfPZsp3btTuWhRjl6+TOD33+Pu6kp0bCx3oqIeOmbX++8/9PnV556jStGifPDjj0zdvJkP7P3bHqXfokWUzp+fIc2bP7JchUKFOPrRRxy7HNf12b9IEdxdXTl2+TLjf/qJNQMHkt3Dg5lbtzIzOJjb9+7xQpUq/LtLF7InMXAjKxARBtSpw9B161j87be89PLLVoeknNTjauYGEjca9DKwAygP1CVuKa/OaRuaUmlnzZo1HN28mZnt2+Mijpw+0flFpPMAiP0XLlDQ25vC8ZKY+/8ij5rUvF2VKlQvUYJNx4/Ts1YtpvbokWzZ++eJ/y99+upVapUqlaj/VmEfnySn+UjtNe/L5u5Os4oVH1vuceqXL09Qnz4EBAXRdvp0IC7BfLNePSoVLszKgwfxTsG/2bCWLRmzZg1rDh9+bDL37c6dbAgJYdu776ZoBKy7qyv/iFdraIyhz7ff8mKtWjSrWJEle/YwdNky5rz6KsXz5OGf33xDrDHMfOmlx547s3JzceGz5s1545tvKOfnR+14g1uUSqnHJXOvAiHAs8aY2wAi8l/gnyKS2xhzM60DVMrRQkJC+O8XXzC/Uyc8tJ9KIrfTeWqSA+fPP1QrBzxY5/X6338ne9z3e/dy8ELcdJO5PD0T9SWL7/55Eq4fm9wRySWRqbnmfbE2G1fj1Qg+jm+uXMkOEOhWowadq1Xj8KVL3L53jwoFC1LA25va48bh5uKSaMm1pLi7ulLExyfZKUbui4yOZsiyZbSpXJlC3t6EhoUBcMneLB5+9y6hYWHkz5kz2eR3VnAwp8LCWNW/PxA3BU2XatV4yZ6wvN+6Ne8EBTG9Z88k+wlmFTk8PJjcqhV9hg3jv999RxEnnkJHWeNxyVwF4gYXxP9L9CXQG/ADdqdVYEqlhRs3bjBswACmtWyZqg7gWUl6jma9fPMmf966RbXixR/aXtn+MDtlTyAS2nDsGK/Mm0enatVwd3Vl7m+/MbhZMyoWLpxk+VD7CNXK8R6SZXx9ORkWRqzN9lDy9Ed4OOF37z71Ne+74KA+c/e5urg81Gfuz/BwDpw/T0M/vyTnmUvoXnQ0F2/c4NkyZR5Z7m50NFdv32bN4cOsOXw40f5vd+3i2127+KJLF95t0SLR/ks3bvD+ypXM6tXrQTP3xZs3qVGy5IMyxfPk4V50NH9FRFDA2/uxsWdmRby9+bhRIwb07s13K1eSLR2nBlLO73HJXA4Sz/12Od4+pZxGZGQk/V5/neF16lAmXz6rw8mwItKxz1xS/eUAqpUogXe2bOw8cybRMbvOnKHzV1/xfNmyLHrjDS7evMny/ft5f+VKfrDXACW08/RpCnp7U8E++AGgwz/+wfj161mwY8eDARAAn69f75Br3ueoPnNJsdlsBCxZQqwxiZpMr0VEPEii4vvwxx+JsdloX6XKg23RsbH8fvUqXh4eD+b6y+HpydK33kp0/NWICPovXkyrSpXo/fzzVCmW5Bg1Bnz3XdwcePGaDYv4+HD40qUHnw9fuoSHm1uiEbhZVY2iRXnZz4+Avn2ZOWcObm6pmQpWZWUp+aYkbG+4/1k7GimnERMTw/CAANoWKkSD0qWtDidDS8/RrPeTuYQ1c64uLnSuVo0fDx0iMjoaT3d3AEL++IO2X36JX4EC/NCvH57u7pT19aX388/z1bZtbA8N5fly5R46V8S9e/wSGsobdes+tH14ixYs3r2bPt9+y77z56lUpAhbT5xgx+nTDyUXT3LN+BzVZy7i3j1qjx9Pp6pVKZ0/P+F37/Ld7t3sO3+esR060LhChYfKf7p2LTtPn6ZxhQoPpnpZe+QIW06coE7p0rzTuPGDspdu3KDi6NE09PNj69ChQFxzbNcaNRLFcX80a1lf3yT3Ayzfv5+fjx/nyKhRD21/uU4d3liwgMAlSyiWJw+frFnDS7VqZekm1oQ6+/tz9tdf+Wz0aP71ySd6b1SKpCSZayMiheJ99iIuoesmIlUTlDXGmMkOi04pB7DZbIwdNYqC4eG8HO8BppKWns2sBy5cILeXF2WSmIKkX8OGfLNjB//38GG6VK/O+evXaTF1Kj7Zs7MuIADveM3ko9q1Y/6OHQxfsYLtw4c/dJ7lBw5wJyqKvgmWTsqTIwe/DBvGkKVLWbBzJ8YYGvn5sWXoUJpOjvsz9qTXTAsebm5UKVqUxbt380d4OF4eHtQqVYr1AQG0rFQpUflGfn4c++MP5u/cybWICFxdXChfoABjO3RgSPPmZLMnyI4Wfvcu7ySzZNdrzz3HH+HhzAoO5u+oKDpWrZqiQSRZiYgwuF49hq1Zw6ypUxkweLDVISknII8aLSYitlSezxhjMmSP8po1a5q9e/daHYZKZ8YYJowbx419+/i0RQsduZoCDSdMYNupUyzv25fO1as/8Xkio6MZGBTEpuPHCbt9m8I+Pgxo2JBA+4S7KdFq6lT+joril2HDnjiOGmPHUjJvXlY85RqvSqWnGJuNgT/+yLNdu/LP3r2tDkdZQET2GWNSNHfW42rmtBpDObVZ06dzedcuvmjdWhO5ZJy+epXdZ89SvUQJ/AoWfDDKMbkRiikVY7NRyNubDYMGUSZ/fv536RItp06lsI8PPZJZLSGhid268Y9PPmHDsWO08PdPdQw/HDzI4UuXCHrzzVQfq5SV3FxcmNKuHW8vWULOXLnoap+AWamkPLJmLjPRmrmsZ+H8+exYupQpbdvqFCSPsGzfPrrNns3ARo0Y2aYNJUaMIMZm4/y4cRSPt/C9I7wxfz45PT2Z1rOnQ8+rVGb1d1QUfX78kVeHDKFV69ZWh6PSUWpq5rRnpcqUVixfzuagICa2bq2J3GO08PenkLc3M4KDqTBqFDE2Gy39/R2eyMXExvJraGiyox+VUonl8PBgZrt2zJkwgW3btlkdjsqgNJlTmc769etZPns2U1u3JnsadfLOTLyzZ2dlv348U7Qori4u9KlXj6A+fZItHxkdTcS9e8m+Ym1Jd7UNWLIEn+zZefXZZ9PqR1EqU8qdPTsz2rZl8pgx7Nmzx+pwVAakzawqU9m8eTP/GTeOWW3bkvcp+3yppL08Zw6Ldic/X/iWIUNolGCajKFLl7IxJITNQ4bonGJKPaGL4eEMWLeOMZMmUbVqwskkVGaTmmZWTeZUpvHLtm1M+egj/vvCC5rIZSCBS5aw6fhxNg8Zkmg5LaVU6lwID6f/mjWMmz6dypUrWx2OSkPaZ05lOTt++42JH37If9q310QuAwkICuJnTeSUcpjiPj5Mb92a9/r35/jx41aHozIIrZlTTm/Pnj18MmQIczp1wleb8DKMc9euUWrkSDzd3HCLNwilfrlyrAsIsDAypZzf2evXGbB2LVPmzKF8+fJWh6PSgDazJkGTucxp/759jB40iK87daKg1vwopbKQ369dY9C6dUyZO5dyj1hSTjknbWZVWcLWLVsYExjI7I4dNZFTSmU5ZfPlY1LLlgS+8QaHDh2yOhxlIU3mlFNatnQpsz79lHldulDY29vqcJRSyhJ+vr581a4dowcNYuuWLVaHoyzyuOW8lMpQjDF8OWUKRzdt4uuOHcnl6Wl1SEopZaliuXMzp2NHAj77jD/++IMXX3rJ6pBUOtOaOeU0bDYbHwwfzpUdO5jWpo0mckopZZfPy4vZHTrwa1AQE//9b7JKf3gVR5M55RQiIyN56/XXKXTtGmOaNMHTTSuVlVIqvhweHkxu3ZrbBw4wPDCQmJgYq0NS6USTOZXh3bx5k5e7daO5tzfv1KmDm4t+bZVSKikerq582LAhpf/+mzdffZW7d+9aHZJKB5Y+FUWklYicEJFQERmRxH5PEVli379LRErZt5cSkbsictD++iq9Y1fp49y5c7zStSsD/P3p8cwziIjVISmlVIbm6uJCv1q16FCwIC9368a1a9esDkmlMcuSORFxBWYArQF/4EUR8U9QrDdwwxhTDpgMfB5v3+/GmKr219vpErRKV6GhofT/5z/5rH59GpUpY3U4SinlNESEThUrMrhKFV7r0YOrV69aHZJKQ1bWzNUGQo0xp40xUUAQ0CFBmQ7AfPv7ZUBT0aqZLOHQoUNMnTqVt1u35pnCha0ORymlnFK9UqXo1bQpH330EWfOnLE6HJVGrEzmigIX4n2+aN+WZBljTAwQDuSz7ystIgdEJFhE6qd1sCp9GGOYN28eP/30E2PHjsVDBzoopdRT8cqWjS+++IJ58+axcuVKq8NRacDKZC6pGraEY6mTK/MHUMIYUw0YAiwWkUQzx4rIWyKyV0T2ahVzxhceHs6wYcMoU6YMw4cPx0UHOiillEN4eHjw8ccfIyJ8+OGH3Lt3z+qQlANZ+bS8CBSP97kYcDm5MiLiBvgA140xkcaYawDGmH3A74BfwgsYY2YbY2oaY2r6+vqmwY+gHGXXrl2MHj2aESNG0LBhQ6vDUUqpTKljx4706dOHd999l5CQEKvDUQ5iZTK3BygvIqVFxAPoCaxKUGYV8Jr9fVdgszHGiIivfQAFIlIGKA+cTqe4lQPZbDamTp3K/v37mTx5Mvnz57c6JKWUytRKlCjBlClTWL16Nd98841OMJwJWJbM2fvADQR+AkKA740xR0XkYxF5wV5sDpBPREKJa069P31JA+B/InKIuIERbxtjrqfvT6Ce1pUrVwgMDKRBgwb069dPpx1RSql04ubmxvDhwylZsiTDhg0jPDzc6pDUU7C0d7kxZi2wNsG2UfHe3wO6JXHccmB5mgeo0szGjRvZtGkTY8eOJVeuXFaHo5RSWVLjxo155plnGD16NL169aJWrVpWh6SegPYwV+kqOjqasWPHEhYWxvjx4zWRU0opi+XPn5/JkyezZ88epk2bhs1mszoklUqazKl0c/ToUQYPHkz37t3p1auX1eEopZSyExH69+9PvXr1CAwM5OzZs1aHpFJBJ/FSae7WrVsPBjdMnjwZd3d3q0NSSimVhOrVq1OxYkWmT58OwDvvvEO2bNksjko9jiZzKs0YY1i8eDGHDx8mMDCQQoUKWR2SUkqpx8iePTvDhg3jzJkzjBw5ksaNG9O+fXurw1KPoM2sKk0cOnSIQYMGUapUKcaPH6+JnFJKOZnSpUszadIkXF1dGTx4ML///rvVIalkaM2ccqibN28yefJkChcuzKRJk3DT5biUUsqptWnThiZNmjBjxgyio6MJCAjAy8vL6rBUPPqkVQ5hs9lYuHAhJ06cIDAwkAIFClgdklJKKQfJli0bQ4cO5dy5c4waNYp69erRoUMHnR80g9BmVvXUduzYQWBgIBUqVOCzzz7TRE4ppTKpkiVLMmHCBLy8vBgyZAiHDx+2OiSF1sypJ2SMYfPmzaxZs4Znn32WyZMn4+rqanVYSiml0kGLFi1o1KgRixYtYsGCBXTt2pU6depYHVaWpcmcShWbzcbq1asJDg6madOmTJw4UavZlVIqC/Lw8OD1118nNjaWZcuW8f3339O2bVsaN26sz4V0ps2sKkViYmJYtGgRw4YNI3fu3EycOJG2bdvqL6xSSmVxrq6u9OjRgwkTJnDnzh2GDh3KqlWrdCWJdKQ1c+qRIiMjWbBgASdPntSVG5RSSiVLRGjXrh1t27YlODiYYcOGUbNmTbp166YzG6QxvbsqSWFhYSxatIgrV67wyiuv0KdPH6tDUkop5QREhEaNGtGoUSN2797N+++/T9myZenZsye5c+e2OrxMSZM59UBUVBRr1qxhx44dFCxYkB49elCsWDGrw1JKKeWkateuTe3atQkNDWXmzJncunWLxo0b06xZMx0050CazCkOHjzIypUriY2NpW3btnz++efaF04ppZTDlCtXjpEjR2Kz2di6dSsffvghXl5edOvWjQoVKlgdntPTZC6LCgsLIygoiEuXLlG1alVGjBhB9uzZrQ5LKaVUJubi4kKTJk1o0qQJt27dYunSpcydO5eyZcvSo0cPfHx8rA7RKWkyl4WEhYWxfv16jh49iq+vLz179tRmVKWUUpbw9vamd+/eAJw6dYoZM2Zw69YtqlevTosWLbR/XSpoMpeJ2Ww29u3bx88//8zt27cpUKAArVq14pVXXtFmVKWUUhlG+fLlGTlyJMYYDh06xOzZs7l58yZ58+alZcuWVK5cWZ9bj6DJXCZz48YNNm7cyKFDhxARatasycCBA8mVK5fVoSmllFKPJCJUrVqVqlWrAnD9+nU2bNhAUFAQIkKtWrVo2rQpOXPmtDjSjEWTOScXHh7O7t272bt3L7dv3yZPnjy0aNGCbt266f9ilFJKObW8efPSs2dPevbsSWxsLHv37mXatGlERESQJ08eateuTc2aNcmRI4fVoVpKkzknYrPZCAkJYefOnZw9exaI63NQp04dAgICsvyXWSmlVObl6upKnTp1HqwBGx4ezp49e5g2bRp37twB4pprn3vuOcqVK5elKjQ0mcugbDYbFy5c4MiRIxw4cIDIyEhEhIoVK9K0aVNKliyZpb6oSimlVHw+Pj40a9aMZs2aps3uUgAABo5JREFUAWCM4dSpU+zYsYMFCxYA4OXlRY0aNahUqRJFihTJtM9NTeYsZrPZOHv2LMeOHSMkJITbt28Dcf0GSpQogb+/P0OHDtVpQ5RSSqlHEBH8/Pzw8/N7sC0iIoIDBw6wevVqLl++/GB77ty58ff3x9/fn+LFizt9kqfJXDqIjIzk/PnznDt3jnPnznHp0iViYmKAuDl3SpUqhb+/Pw0bNtSBCkoppZSD5MyZk/r161O/fv2Htt+4cYOQkBA2bNjAhQsXMMYA4OHhQbFixShZsiQlS5akWLFieHh4WBF6qliazIlIK2Aq4Ap8bYwZn2C/J7AAqAFcA3oYY87a970P9AZigQBjzE/pGHqSTp48yYYNG7h69epD2z09PSlevDglS5akWbNmFClSBHd3d4uiVEoppbK2PHnyULduXerWrfvQ9qioKC5evMi5c+fYtm0bFy9eJDo6+sF+EaFgwYK0a9eO4sWLp3fYybIsmRMRV2AG0By4COwRkVXGmGPxivUGbhhjyolIT+BzoIeI+AM9gUpAEeBnEfEzxsSm70/xsHz58tG9e3d8fX2dvspWKaWUymo8PDwoU6YMZcqUSXK/zWbjypUreHl5pXNkj+Zi4bVrA6HGmNPGmCggCOiQoEwHYL79/TKgqcRlSR2AIGNMpDHmDBBqP5+l8uXLR4ECBTSRU0oppTIhFxcXChcunOGWHbOymbUocCHe54tAneTKGGNiRCQcyGffvjPBsUXTLlRlBRHhnqsrv4WHWx2KUko5LZPBapGU41mZzCVVfWVSWCYlxyIibwFv2T9GiMiJVEX4ZPIDf6XDdbIKvZ+Op/fUsfR+Op7eU0cbOFDvqWOlx/0smdKCViZzF4H4vQeLAZeTKXNRRNwAH+B6Co/FGDMbmO3AmB9LRPYaY2qm5zUzM72fjqf31LH0fjqe3lPH03vqWBntflrZZ24PUF5ESouIB3EDGlYlKLMKeM3+viuw2cSNH14F9BQRTxEpDZQHdqdT3EoppZRSGYZlNXP2PnADgZ+Im5pkrjHmqIh8DOw1xqwC5gALRSSUuBq5nvZjj4rI98AxIAYYYPVIVqWUUkopK1g6z5wxZi2wNsG2UfHe3wO6JXPsWGBsmgb4ZNK1WTcL0PvpeHpPHUvvp+PpPXU8vaeOlaHup9yf9VgppZRSSjkfK/vMKaWUUkqpp6TJXBoQkU9E5H8iclBENohIEatjcmYi8oWIHLff05UiktvqmJydiHQTkaMiYhORDDMiy9mISCsROSEioSIywup4nJ2IzBWRMBE5YnUsmYGIFBeRLSISYv99H2R1TM5ORLKJyG4ROWS/p2Osjgm0mTVNiIi3MeaW/X0A4G+MedvisJyWiLQgbiRzjIh8DmCMec/isJyaiFQEbMB/gHeNMXstDsnp2JckPEm8JQmBFxMsSahSQUQaABHAAmNMZavjcXYiUhgobIzZLyK5gH1AR/2OPjn7KlQ5jDERIuIO/AoMMsbsfMyhaUpr5tLA/UTOLgdJTGisUs4Ys8EYE2P/uJO4eQXVUzDGhBhj0mMS7cwsJUsSqlQwxmwjbuYC5QDGmD+MMfvt728DIehqSU/FxImwf3S3vyx/xmsyl0ZEZKyIXAB6AaMeV16l2BvAOquDUIqklyTUB6XKkESkFFAN2GVtJM5PRFxF5CAQBmw0xlh+TzWZe0Ii8rOIHEni1QHAGPOBMaY4sAgYaG20Gd/j7qe9zAfEzSu4yLpInUdK7ql6KilaVlApq4lITmA5EJig5Ug9AWNMrDGmKnGtRLVFxPIuAZbOM+fMjDHNUlh0MbAGGJ2G4Ti9x91PEXkNaAc0NdrRM0VS8R1VTyZFywoqZSV7v67lwCJjzAqr48lMjDE3RWQr0AqwdNCO1sylAREpH+/jC8Bxq2LJDESkFfAe8IIx5o7V8Shll5IlCZWyjL2z/hwgxBgzyep4MgMR8b0/o4KIZAeakQGe8TqaNQ2IyHKgAnGjBc8BbxtjLlkblfOyL+fmCVyzb9qpo4Ofjoh0Ar4EfIGbwEFjTEtro3I+ItIGmML/X5IwI65K4zRE5DugEZAfuAKMNsbMsTQoJyYi9YBfgMPEPY8ARtpXX1JPQESqAPOJ+513Ab43xnxsbVSazCmllFJKOTVtZlVKKaWUcmKazCmllFJKOTFN5pRSSimlnJgmc0oppZRSTkyTOaWUUkopJ6bJnFJKKaWUE9NkTimllFLKiWkyp5RSSinlxP4fQA73Sr3NyOUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -2, 2 # integral limits\n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-2}^{2} f(x)\\mathrm{d}x = $\" + \"{0:.1f}%\".format(result_n2_2*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "ax.set_title(r'95% of Values are within 2 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/95_2_std.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "95% of the data is within 2 standard deviations (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Within 3 Standard Deviations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Math Expression</b> $$\\int_{-3}^{3}\\frac{1}{\\sqrt{2\\pi}}e^{-x^{2}/2}\\mathrm{d}x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9973002039367399\n"
     ]
    }
   ],
   "source": [
    "# Make the PDF for the normal distribution a function\n",
    "def normalProbabilityDensity(x):\n",
    "    constant = 1.0 / np.sqrt(2*np.pi)\n",
    "    return(constant * np.exp((-x**2) / 2.0) )\n",
    "\n",
    "# Integrate PDF from -3 to 3\n",
    "result_n3_3, _ = quad(normalProbabilityDensity, -3, 3, limit = 1000)\n",
    "print(result_n3_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a, b = -3, 3 # integral limits\n",
    "\n",
    "x = np.linspace(-3, 3)\n",
    "y = normalProbabilityDensity(x)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.plot(x, y, 'k', linewidth=.5)\n",
    "ax.set_ylim(ymin=0)\n",
    "\n",
    "# Make the shaded region\n",
    "ix = np.linspace(a, b)\n",
    "iy = normalProbabilityDensity(ix)\n",
    "verts = [(a, 0)] + list(zip(ix, iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='red', edgecolor='0.2', alpha = .4)\n",
    "ax.add_patch(poly);\n",
    "\n",
    "ax.text(0, .08, r\"$\\int_{-3}^{3} f(x)\\mathrm{d}x = $\" + \"{0:.1f}%\".format(result_n3_3*100),\n",
    "         horizontalalignment='center', fontsize=18);\n",
    "\n",
    "ax.set_title(r'99.7% of Values are within 3 STD', fontsize = 24);\n",
    "ax.set_ylabel(r'Probability Density', fontsize = 18);\n",
    "\n",
    "fig.savefig('images/99_3_std.png', dpi = 1200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "99.7% of the data is within 3 standard deviations (σ) of the mean (μ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Infinity to Positive Infinity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For any PDF, the area under the curve must be 1 (the probability of drawing any number from the function's range is always 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>You will also find that it is also possible for observations to fall 4, 5 or even more standard deviations from the mean, but this is very rare if you have a normal or nearly normal distribution.</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Boxplot Documentation Used"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "General boxplot documentation: https://matplotlib.org/api/_as_gen/matplotlib.pyplot.boxplot.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Changing Color of Boxplot: https://matplotlib.org/examples/statistics/boxplot_color_demo.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Properties of a box plot: https://matplotlib.org/examples/statistics/boxplot_demo.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How I plotted over multiple subplots: https://stackoverflow.com/questions/6146290/plotting-a-line-over-several-graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Back No Border but have background for ax text: https://stackoverflow.com/questions/27531290/remove-matplotlib-text-plot-border"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
